Right-hander Andrew Cashner (2-5) combined with three relievers to help the Orioles win for just the second time in their last six games.
Machado hit his 15th home run of the season in the fourth inning and Trumbo added his second in the fifth, staking Baltimore to a 2-0 lead.
The White Sox threatened to erase the deficit, and perhaps even go ahead, in the bottom of the fifth, only to be denied by Mancini.
Adam Engel hit a one-out single, but was gunned down trying to stretch it into a double by Mancini.
Yoan Moncada then walked and Yolmer Sanchez singled before Jose Abreu doubled to left field to get the White Sox within 2-1.
But Sanchez also tried to score on the play and was thrown out by Mancini, allowing the Orioles to retain the lead.
The two outfield assists raised Mancini's season total to six, tops among all left fielders in the majors.
Jones homered in the sixth, his eighth of the season, to make it 3-1, before the White Sox rallied again in the bottom of the inning.
This time, a pair of ground-rule doubles by Daniel Palka and Leury Garcia sandwiched a single by Matt Davidson, scoring a run and putting runners at second and third with no outs.
With the lead having been trimmed to 3-2, the Orioles summoned Mychal Givens from the bullpen. He prevented further scoring by getting a popout and two strikeouts.
Givens also pitched a hitless seventh and Richard Bleier a scoreless eighth, setting the stage for closer Brad Brach, who worked out of a bases-loaded jam in the ninth, striking out Trayce Thompson to end the game and register his seventh save.
The Baltimore bullpen pitched four shutout innings, allowing two hits and striking out five.
Cashner allowed two runs and eight hits in his five-plus innings. He walked three and struck out four.
White Sox starter Hector Santiago (0-2) allowed just five hits in six innings, but three were home runs that produced all the Baltimore scoring. He walked two and struck out seven.
Abreu had two doubles while Davidson and Garcia added two hits apiece for the White Sox, who lost for just the second time in five games to begin an eight-game homestand.
The White Sox out-hit the Orioles 10-5 in defeat.
--Field Level Media
Baltimore | Chi. White Sox | |
Andrew Cashner | Player | Hector Santiago |
Win | W/L | Loss |
5.0 | IP | 6.0 |
4 | Strikeouts | 7 |
8 | Hits | 5 |
3.60 | ERA | 4.50 |
Baltimore | Chi. White Sox | |
Adam Jones | Player | Matt Davidson |
1 | Hits | 2 |
1 | RBI | 0 |
1 | HR | 0 |
4 | TB | 2 |
.333 | Avg | .667 |
Team | Hits | HR | TB | Avg | LOB | K | RBI | BB | SB | Errors |
Baltimore | 5 | 3 | 14 | .161 | 11 | 12 | 3 | 3 | 1 | 0 |
Chi. White Sox | 10 | 0 | 14 | .286 | 19 | 9 | 2 | 5 | 0 | 0 |