The magic number for the White Sox to clinch the division remained at two games.
Reyes had four of Detroit's 16 hits. Daz Cameron reached base four times and scored two runs for the Tigers, who have won the first two games of the three-game series.
''Just seems like we're not catching breaks, but we're not putting ourselves in a lot of positions to be able to get wins,'' said Chicago starting pitcher Dallas Keuchel, who gave up two runs on 11 hits in five innings. ''That's not a great combo to have right now.''
The White Sox have lost five of their last seven games and manager Tony La Russa is concerned that his team is ''treading water'' as the postseason approaches.
''We have to win at a higher percentage than we're winning right now,'' he said. ''You've got to be able to execute in this league. Our execution is not where it has to be in all phases.''
Bryan Garcia (3-2) pitched 1 1/3 scoreless innings of relief for Detroit starter Tyler Alexander, who went five innings. Michael Fulmer got the last four outs for his 11th save.
''Our team finds ways to win,'' said Detroit manager A.J. Hinch, whose team has won four straight and seven of its last nine games. ''We put pressure on the opponent, we hung in there. Today was a really weird game. Both teams left double-digit guys on base. Both teams found a lot of hits (but) had a hard time pushing runs across until the end and we came out with the big hit.''
Jace Fry (0-1) gave up three runs on four hits in 1 2/3 innings of relief of Keuchel. Luis Robert led Chicago's offense with two hits and two RBIs.
Robert gave the White Sox a 2-0 lead in the third with a two-run single through a drawn-in infield. The Tigers scored in the bottom of the inning on Baddoo's RBI single.
Baddoo's second run-scoring hit tied the score at 2 in the fourth.
Detroit nearly took the lead in the sixth when Reyes was called safe at home on Baddoo's fielder's choice grounder. The call was overturned upon video review.
The Tigers broke the deadlock in the seventh on Niko Goodrum's RBI single. Reyes ripped a two-run single to give his team a three-run lead.
''We're all going in the same direction,'' Reyes said through an interpreter. ''Every time we go out on the field, we go out to win, regardless of whoever we're playing.''
Tim Anderson's single in the eighth knocked in the White Sox's final run. Chicago left 13 runners on base.
''We had a chance to blow that game open and score more runs than we did,'' La Russa said.
EARLY BIRD SPECIAL
The game was originally scheduled for the evening but was moved up to 1:10 p.m. due to a rainy forecast.
White Sox: OF Adam Engel was activated from the 10-day injured list and INF Romy Gonzalez was optioned to Triple-A Charlotte.
White Sox: RHP Reynaldo Lopez (3-3, 3.00) is scheduled to start the series finale on Wednesday. Lopez has 13 career starts against the Tigers, posting a 4-4 record and 3.42 ERA in those outings.
Tigers: RHP Casey Mize (7-8, 3.64 ERA) has lost all three of his starts against the White Sox this season. The prized rookie won't be on the mound for long - he's been placed under a three-inning limit.
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