Patron deity of the SDMB Sammy Ogg was in a number of pre-'55 Dragnet episodes after making his television debut on Fireside Theatre in '51 – same year he was on the big screen, in The Day The Earth Stood Still – followed by I Love Lucy in '52, and Our Miss Brooks in '53, and Make Room For Daddy in '54, and The Gene Autry Show in '55, and Annie Oakley in '56, and Schlitz Playhouse in '57, and et cetera.
Robert Duvall was in theater for years and started into television in 1959 on the Armstrong Circle Theater. He’s 83.
Sadly, the OP puts the cut-off date at '58. So an Armstrong Circle Theatre alum like Luke Halpin counts, since he picked up Studio One In Hollywood work in '55 and '56 and '57 – and played Jake Oakley in a TV movie of Annie Get Your Gun before the deadline likewise – but not because of his years acting on Flipper in the '60s, or his movie roles in the '70s, or his stunt work in the '80s and '90s and '00s, and so on.
Kevin Corcoran made his TV debut in '53, on Ford Television Theatre; in '54, he was on the big screen with Jimmy Stewart for The Glenn Miller Story; in '55, Untamed with Tyrone Power; and in '56, back on television for December Bride before showing up in '57 on Walt Disney’s Wonderful World of Color.
Most recent acting credit in '09, but he’s apparently been busy since – racking up behind-the-scenes credits on Sons of Anarchy just like he did on The Shield before it, and just like Crossing Jordan before that, and so on back through Providence and Profiler and Murder She Wrote and Quantum Leap and Baywatch and Simon & Simon and Scarecrow and Mrs King and et cetera.
Oh, and pre-'58 he was a castmember on The New Adventures of Spin and Marty as well as, y’know, Further Adventures of Spin and Marty.
David Stollery made his TV debut in 1950, on Fireside Theatre, and promptly racked up a bunch of pre-'58 television credits: on Celebrity Playhouse, with Joseph Cotten; and The Gale Storm Show, with Morey Amsterdam; and The Ray Milland Show, with, uh, Ray Milland; and I Love Lucy, with – okay, you get where this is going, right?
Anyhow, throw in a Henry Ford TV movie, and work on Studio 57, and a role on Dragnet, and so on, right up to the deadline, sure as he’s still with us now.
Fay McKenzie is still with us, after her work on episodes of The Colgate Comedy Hour pre-'54 and her work in all those Gene Autry movies pre-'44 – and she did dozens of movies back in the '30s, after doing yet more in the '20s, after making her screen debut in a silent film back in 1918.
George Cole was in a few TV movies before he did a 1957 episode of Suspense before acting in a bunch of Walt Disney’s Wonderful World of Color episodes in the '60s; next year, he’s set to (a) turn ninety, and (b) return to the big screen.
(No, I’m not using “return to the big screen” as a euphemism for “die”; I’m referring to how he acted in plenty of movies back in the '40s, before getting the leading role on a radio sitcom starting in '53; he also picked up plenty of stage credits; go check out his autobiography some time, it only just hit the shelves a matter of months ago.)
Julie Newmar of course did plenty of TV work in the '60s – on Star Trek and Batman and Get Smart and The Beverly Hillbillies after starring in My Living Doll – but only after making her small-screen debut back in '57, on The Phil Silvers Show.
Oh, good one. Inspired me to check Mamie Van Doren’s IMDb page. Yup, she qualifies. Well, sort of. Really stretching there.
Hey, you know who likewise appeared as the mystery guest on What’s My Line before the cut-off date? And who, like Van Doren, appeared on both Lux Video Theatre and The Steve Allen Plymouth Show pre-'58? But who, instead of making the rounds on The Linkletter Show and The Ray Anthony Show like Van Doren did, busily made the rounds on The Frank Sinatra Show and The Bob Hope Show and The Ed Sullivan Show before the end of 1957?
Now in her nineties, Kathleen O’Malley has movie credits stretching back to the '20s, with TV work from The George Burns And Gracie Allen Show in '51 to Racket Squad in '52, The Abbott and Costello Show in '53, The Loretta Young Show in '54 – and so on for The Man Called X and Navy Log and The Millionaire and Schlitz Playhouse and Wagon Train and The Life and Legend of Wyatt Earp before the deadline – after which, she spent the rest of the '50s continuing to work on small-screen westerns: Rawhide, Maverick, Bronco, Laramie, Tales of Wells Fargo, you name it.
You maybe remember her from that Chris-Farley-and-David-Spade flick in the '90s?
Well, no, not anymore. 
Olive Sturgess, who was credited alongside her in half-a-dozen of those Bob episodes in '57 and '56 – and who got lots of work in '55, on Matinee Theatre and Studio 57 and Front Row Center and The Millionaire and Shower of Stars and et cetera – is apparently still with us.
Still, RIP And-Ann-B-Davis-As-Alice.
Since there’s another Hobbit movie on the way for later this year, Ian Holm is still acting decades after his Oscar-nominated work in Chariots of Fire, decades after performing in a made-for-TV version of Rope back in '57.
In '59, he and fellow future Tony winner Roy Dotrice appeared in a made-for-TV version of A Midsummer Night’s Dream; Dotrice had previously acted on a number of TV shows (and a TV movie of Treasure Island) back in '57, sure as you’ve maybe seen him recently on Game of Thrones.
Incidentally, the guy playing Oberon in that production was Robert Hardy, who made his small-screen debut way back in '51 before playing Cassio in a TV movie of Othello in '55 and playing David Copperfield in over a dozen episodes during '56; he’s got a movie role in the works for later this year likewise.
As per IMDB, June Whitfield’s most recent acting credit was back in March, long after her television debut back in 1951; she then did a couple of TV movies before the end of 1957, popping in on half-a-dozen TV shows along the way – not counting her work as a small-screen voice actress, you understand – and then kept on keeping on; right after the OP’s cut-off date, you could see her on This Is Your Life in '58, right before she spent the better part of a century busily racking up TV and movie roles.
Has June Foray been mentioned yet? She started her career so long ago she was an established radio star before television began. And she’s still working. (Her age is uncertain as she’s “adjusted” her birth year a few times. But she’s apparently 96.)
The Pat Boone Chevy Showroom aired from October 3, 1957 to June 23, 1960. And Pat is still with us (for now).
Carleton Carpenter, who went from Broadway to the big screen in the '40s, was in a made-for-TV movie in '54 before making the rounds in '55 – on Goodyear Playhouse and The Alcoa Hour and The Best of Broadway, and General Electric Theater, plus a recurring role on Luke and the Tenderfoot.
He kept racking up credits in '56 and '57 – not to mention '58 and '59, and on through the '60s and '70s and '80s – and as per IMDB is (a) still alive, and (b) set to appear in a documentary later this year.
Has Mary Tyler Moore been mentioned? In different sources, I see her TV debut as a dancer ranging from 1952 to 1956. The earliest thing I personally have ever seen her act in was a 1959 episode of Steve Canyon. She only had a very brief walk-on part, but I recognized her instantly!
This apparently was her TV debut on the Ozzie and Harriet Show:
DOB for MTM: 29 December 1936.Sherry Alberoni has all kinds of TV credits from '58 on: she’d work on a western, she’d get recurring roles on sitcom after sitcom, she’d join the cast of a soap opera; she was even the voice of Wendy on SuperFriends; but before all of that, she was a Mickey Mouse Club Mouseketeer before doing an Abbott and Costello movie in '56.