Jack Hannahan also homered for the A's, who have won two in a row for only the second time since the All-Star break.
The game was supposed to be the latter part of a split doubleheader, but the afternoon contest was wiped out by rain, courtesy of Tropical Storm Hanna. No makeup date was announced.
If the game is not made up, Oakland will finish with a 5-0 sweep of the season series. The A's swept the Orioles once before, 7-0 in 2004, which was also their last sweep of an AL foe.
It was the third multihomer game of the season for Cust, who also had a sacrifice fly. His 27 homers are a career high, surpassing the 26 he hit with Oakland last year.
Smith (7-14) allowed three hits, walked five and struck out two. The left-hander was 1-8 since June 30 and had yielded a total of 13 runs in his last two starts.
Huston Street gave up a run-scoring grounder to Nick Markakis in the eighth.
Orioles starter Daniel Cabrera (8-9) allowed two runs, five hits and six walks in three-plus innings. The struggling right-hander missed the strike zone on half of his 84 pitches.
One night after Orioles pitchers issued 10 walks in an 11-2 loss, Cabrera walked the first three batters before Cust hit a sacrifice fly. Oakland then reloaded the bases before Hannahan grounded out on a 3-1 pitch.
Baltimore stranded a runner at third in the bottom half, then left the bases loaded in the second.
Cust led off the third with a no-doubt shot to right on a 3-2 count.
In the fourth, Baltimore's Alfredo Simon began his major league career by getting Kurt Suzuki to hit into a double play. Four pitches later, however, Cust sent a fastball into the right-field bleachers for a 3-0 lead.
Hannahan connected in the fifth on a 3-1 pitch, his eighth homer of the season -- all against right-handers. Later in the inning, Rajai Davis chased Simon with an RBI triple.
The doubleheader was scheduled so the teams could avoid playing Sunday, when the Baltimore Ravens open the NFL season at home. As a result, Oakland will have its first Sunday off since Sept. 17, 2000. ... Cabrera took over the team lead in homers allowed (23). ... Baltimore hasn't won a season series against Oakland since 1998.