Jimenez' home run, a solo shot, came in the second to go up 3-0 on Tigers' starter Adam Bernero, who settled down and kept the Sox off the board, pitching through the seventh.
The three runs was more than enough for Loaiza, who retired the Tigers in order into the fourth with one out, when Shane Halter singled to break up the no-hitter.
Loaiza retired the next two batters and kept the Tigers hittless the rest of the way with the exception of a Ramon Santiago bunt single in the sixth.
Ordonez tagged up at second and reached third on the fly, which was one of many hustle plays by Ordonez, who earlier tagged up and reached third on a fly out to left, beat out an infield single, and stole second base, advancing to third on the bad throw by Tigers' catcher Matt Walbeck.
Loaiza left following the eighth, finishing the game with three strikeouts and 100 pitches and was replaced by Billy Koch. Koch retired the Tigers 1-2-3 to end the game.
Josh Stewart will take the mound on Saturday for the second of the three-game set. Stewart, who gave up two runs in 6 2/3 innings in his first start against Detroit, will face righty Nate Cornejo. Gametime is at 12:05 p.m. CT and will be televised on WGN.