(Forrest Gump also won and was the highest grossing film in 1994.)
Probably 1982.
(Lists of best picture nominees where most were in the top 20 highest grossing domestic films of the year. The number before each title is their box office yearly ranking. I’ve only included the higher ranking nominees.)
1982:
1 E.T.: The Extra-Terrestrial Uni. $329,397,487
2 Tootsie Col. $100,768,069
11 The Verdict Fox $39,691,104
12 Gandhi Col. $11,861,444
1991:
3 Beauty and the Beast BV $145,863,363
4 The Silence of the Lambs Orion $130,742,922
16 The Prince of Tides Col. $59,335,243
17 JFK WB $58,112,996
1997:
1 Titanic Par. $338,710,764
6 As Good as It Gets Sony $92,637,620
7 Good Will Hunting Mira. $68,865,287
24 L.A. Confidential WB $39,738,569
2000:
4 Gladiator DW $186,610,052
12 Crouching Tiger, Hidden Dragon $128,078,872 12/08
13 Erin Brockovich Uni. $125,595,205
15 Traffic USA $71,208,084
2010 (ten nominees)
1 Toy Story 3 BV $415,004,880
6 Inception WB $292,576,195
13 True Grit Par. $138,507,277
18 The King’s Speech Wein. $135,453,143 11/26