Tillman (1-0) gave up five hits, including Torii Hunter's solo homer in the fourth, in 8 1-3 innings. Tommy Hunter entered with one out in the ninth and Victor Martinez on second base and retired the last two batters for his second save.
Baltimore won for the first time since its opener against baseball's last undefeated team.
Verlander (0-1) gave up two runs on five hits and two walks over eight innings. He struck out three, moving past Tommy Bridges and into fourth place on the franchise's all-time list with 1,674 in his career.
Baseball's replay system was temporarily unavailable early in the game. Both managers were informed of the technical difficulty during the first inning and it was repaired.
Tillman had more strikeouts (five) than the Tigers had hits (four) against him through eight innings, keeping a crowd of 34,261 quiet on a partly cloudy afternoon in the 50s.
After Tillman got Cabrera to ground out for the first out in the ninth, he gave up a double to Martinez that brought the fans to their feet. Hunter then struck out Austin Jackson for the second out of the inning and got Tyler Collins to bounce out for the last one.
Torii Hunter homered for the third straight game to make it 1-0 Tigers.
Baltimore tied it at 1 in the sixth inning when Nelson Cruz doubled home Jones, who also hit a double. The Orioles went ahead 3-1 in the ninth after Al Alburquerque replaced Verlander and allowed Matt Wieters to hit his first homer of the season.
The Tigers scored 17 runs and had 30 hits in the previous two wins against Baltimore, but were kept quiet at the plate in the series finale.
Miguel Cabrera, who entered the game hitting a baseball-best .398 against Baltimore in his career, went 1 for 4 with a sharply hit single in the sixth.
NOTES: The Tigers planned to fly after the game to California, where they will play the Los Angeles Dodgers on Tuesday night. ... The Orioles stay on the road to play the New York Yankees on Monday afternoon. ... Manager Brad Ausmus was the first to begin his career with four straight win since Clint Hurdle of Colorado and Jerry Royster of Milwaukee both did it in 2002.