But in the end, all it took was a 10th-inning double by Blue Jays designated hitter Adam Lind to ruin the best performance of Tillman's young career, sending the Orioles to a 3-2 loss on Saturday at Rogers Centre.
With Baltimore reliever Danys Baez on the mound in the 10th inning, Toronto's Joe Inglett hit the ball hard at second baseman Ty Wigginton. It kicked off Wigginton's glove, and Inglett was safe at first.
After Marco Scutaro reached on a fielder's choice, Aaron Hill poked a pitch just out of Wigginton's reach into shallow center field for a single.
"The first one hit off the heel of my glove. I should've made that play," Wigginton said. "The second ball got in the lights. I was actually surprised it hit my glove. It is what it is, and it's unfortunate that we didn't find a way out of it."
Lind then fired a pitch from Baez (4-6) deep into left field, cashing in the winning run for the Jays. The Orioles (46-64) have gone 6-16 since the All-Star break.
Tillman pitched well enough to win his first game in three Major League starts, but the Orioles were unable to come up with hits with runners in scoring position, missing several opportunities to break open a game that was locked at 2-2 for much of the afternoon.
Tillman allowed a two-run home run to Alex Rios in the second inning, but he shut out the Jays (52-57) for the remainder of his 6 2/3 innings. Tillman gave up four hits, walked three and struck out four as he pitched into the seventh inning for the first time in the big leagues.
"He said he had trouble getting loose in the first inning, but, boy, he sure pitched a whale of a game using his secondary pitches," Baltimore manager Dave Trembley said. "It seems like the longer he goes in the game, his fastball gets better velocity-wise.
"His breaking ball and his changeup were better than they were [on Monday] in Detroit. They were marginal his first outing against Kansas City. They were a little better against Detroit.
"His curveball and his changeup [were] very good [today]."
Tillman said he felt "drained," adding that he might have overdone it in a bullpen session on Friday.
"I just felt real worn out," he said. "The first couple of innings, I wasn't feeling so good. My whole body just felt drained.
"After the third inning, I definitely loosened up a ton. ... [I] got more confidence in my stuff."
Tillman added that catcher Matt Wieters helped him get through his early inning struggles.
"I feel like me and Wieters had a good connection today," Tillman said. "I pretty much could tell you exactly what he was going to throw down between his legs. We were on exactly the same page once we moved on after that second inning."
After a single and back-to-back doubles in the fourth inning pulled Baltimore out of a 2-0 hole, the offense came up short when given several chances to take the lead in the sixth and seventh innings.
Blue Jays starter Brett Cecil left after 4 1/3 innings due to a left knee injury, and left-hander Brian Tallet came on in relief. Baltimore's Aubrey Huff was hit by a pitch from Tallet to lead off the sixth, and the Orioles loaded the bases on a pair of singles by Melvin Mora and Luke Scott. Tallet induced a popout and a flyout, though, getting out of the inning without surrendering a run.
The Orioles threatened again in the seventh, putting men on second and third, but Tallet got Nolan Reimold to ground out to third, escaping trouble yet again.
Baltimore entered the game batting .298 with runners in scoring position -- good for second place in the American League -- but it went 3-for-14 (.214) in those scenarios on Saturday and stranded 10 runners.
"We definitely had numerous scoring opportunities. ... [We] didn't get the hit," Trembley said. "They made better pitches. [We] didn't get it done."
Although Tillman recorded his first quality start in the Majors, he came away with his third straight no-decision.
"[Tillman] allowed two runs," Trembley said. "He's never faced them before. I thought he made some quality pitches, especially late in the game.
"He pitched good enough, obviously, to win the game."
Erika Gilbert is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.