Olson's hit, his fourth of the game, came off right-hander James Shields, who was pressed into his first relief appearance since 2010 after the White Sox had exhausted nine pitchers in a game that lasted just short of six hours.
Shields retired the first two batters he faced in the 14th before Marcus Semien singled to left field. Jed Lowrie and Khris Davis then worked walks to load the bases, setting the stage for Olson, who already had two doubles, a single and two walks.
Right-hander Lou Trivino (1-0), pitching in just his second major league game, got his first big-league win after throwing three innings of two-hit, shutout relief. He struck out four.
Shields (1-1) took the loss. He was pitching in relief for just the second time in 388 career regular-season and postseason appearances. On June 19, 2010, he got the win by pitching a scoreless 10th inning for the Tampa Bay Rays against the then-Florida Marlins.
On Tuesday, both teams rallied late in regulation play to erase deficits.
Down 6-1 and 9-4 earlier in the game, the A's got a two-out, two-strike, two-run home run by Lowrie off Luis Avilan in the bottom of the eighth to go up 11-10.
Oakland closer Blake Treinen then retired the first two men he faced in the top of the ninth before Welington Castillo's double and Tim Anderson's single kept the White Sox alive at 11-11.
Chicago led most of the way after Yoan Moncada belted his first career grand slam in a five-run second inning. Both teams had tallied once in the first.
Moncada's slam came off A's starter Andrew Triggs, who walked two of the first three batters he faced in the second.
Adam Engel singled in a run before Moncada unloaded his third homer of the season into the right field bleachers, putting Chicago up 6-1.
Moncada finished 2-for-7 with three runs and a career-high-tying four RBIs.
Mark Canha started the Oakland comeback against White Sox starter Carson Fulmer with a leadoff homer in the bottom of the second.
Triggs went just 1 1/3 innings, allowing six runs and five hits. He walked two and did not record a strikeout.
Fulmer, meanwhile, was pulled before he could record an out in the second, having given up four runs on five hits. He also walked two and did not strike out a batter.
Davis had three hits and Lowrie drove in three runs for the A's, who won their fourth in a row.
Semien and Stephen Piscotty added two hits apiece for Oakland, which scored eight or more runs for the third straight game.
Jose Abreu and Delmonico had three hits each for the White Sox, who out-hit the A's 17-16.
Matt Davidson, Yolmer Sanchez and Castillo collected a pair of hits apiece for Chicago, which lost for the ninth time in its past 10 games.
--Field Level Media
Chi. White Sox | Oakland | |
Carson Fulmer | Player | Andrew Triggs |
No Decision | W/L | No Decision |
1.0 | IP | 1.1 |
0 | Strikeouts | 0 |
5 | Hits | 5 |
36.00 | ERA | 40.50 |
Chi. White Sox | Oakland | |
Jose Abreu | Player | Matt Olson |
3 | Hits | 4 |
2 | RBI | 3 |
0 | HR | 0 |
4 | TB | 6 |
.500 | Avg | .667 |
Team | Hits | HR | TB | Avg | LOB | K | RBI | BB | SB | Errors |
Chi. White Sox | 17 | 1 | 23 | .293 | 25 | 11 | 11 | 6 | 5 | 0 |
Oakland | 16 | 2 | 26 | .296 | 22 | 13 | 12 | 12 | 1 | 0 |