DETROIT -- Chris Tillman proved to be more rested than rusty, which turned out to be a delightful occurrence for manager Buck Showalter and the rest of the Baltimore Orioles.

Making his first start since being activated from the disabled list, Tillman outdueled Detroit Tigers' ace Justin Verlander on the latter's home turf, allowing just one run on four hits in six innings to lead the Orioles to a 3-1 win on Sunday in the rubber match of a crucial three-game series at Comerica Park.

The Orioles (78-64) entered Detroit on Friday a game ahead of the Tigers (76-66) for the final wild-card spot in the American League. They left two games up after winning the final two contests of the series.

The biggest reason for the series-finale victory was Tillman, who went on the disabled list after an Aug. 20 start due to shoulder bursitis.

He came off of it in time to help deliver one of the most important starts of the year for the Orioles.

"There definitely was a little bit of rust there," said Tillman, who struck out four and threw 105 pitches. "But I felt like we were able to work our way through it and make pitches when we had to in big situations."

Showalter said on Saturday that he worried that Tillman would be rusty, but felt having roughly three weeks off turned out to be a benefit.

"This time of year, I hope that guys don't get out of sync too much," Showalter said. "I think the rest did him good. We are not out of the woods. We will see how he feels tomorrow and the next day to see if we need to give him that extra day next time we have that ability. But we are going to put our best foot forward each day and see where it leads. Hopefully Chris is a part of that."

On the other side, Verlander picked a bad time to have his first non-quality start since July 7, yielding three runs and seven hits in five innings.

"My arm felt good, but I had only one pitch," Verlander said. "That team likes fastballs and that's all I had, so it was tough out there."

The Orioles took a 2-0 lead in the top of the third on a two-run home run with two outs by Michael Bourn, who deposited a fastball from Verlander over the 365-foot sign in right field.

Bourn entered the game with a .371 career batting average against Verlander (13 of 35), so Showalter put him in the No. 2 spot in the batting order and watched the move pay big dividends.

"It's hard to find any track record against Verlander because he wins the battle most of the time," Showalter said. "But Mike was in position to contribute today and he took advantage of it."

After an easy first two innings, Verlander started to labor in the third, giving up a double to Orioles' No. 9 hitter Caleb Joseph, the home run to Bourn, a single to Manny Machado and a walk to Chris Davis.

Verlander ended up getting out of the jam when he picked off Machado at second base.

The Orioles then got to Verlander again in the fourth when Jonathan Schoop blasted a solo home run to left that gave Baltimore a 3-0 lead.

The Tigers got on the board in the bottom of the fifth when Ian Kinsler laced a two-out single to right to score Justin Upton and cut Baltimore's lead to 3-1.

Detroit had a golden opportunity in the eighth when Miguel Cabrera came up with runners on first and second with one out, but he grounded into an inning-ending double play to cap off an 0-for-9 series at the plate.

Showalter said it was more luck than anything that his pitchers were able to keep the star slugger for the Tigers hitless and that future opponents should be warned that Cabrera is due to break out.

"Somebody is going to have to pay," Showalter said. "I'm glad it's not going to be us."

Orioles closer Zach Britton improved to 41-for-41 in save situations by closing the game out with a scoreless ninth inning, in the process taking over as the saves leader in the American League.

The Orioles ended up holding the Tigers to eight runs in the three-game series.

"Offense is cyclical and we are in a little bit of a funk right now, but you also have to give credit to the Baltimore pitchers," Tigers manager Brad Ausmus said. "They did a great job against us."

NOTES: By virtue of their 11-3 win on Saturday, the Orioles clinched the season series with the Tigers, which could prove to be an important achievement. If the Orioles and Tigers played a one-game playoff to decide a wild-card spot, Baltimore would host based on winning the season series. ... With a series against the team that was behind them in the wild-card standings behind them, the Orioles next will play a three-game series at Boston, the team in front of Baltimore for the first wild-card spot. ... On Saturday night, Tigers 1B Miguel Cabrera drew his 1,000th career walk, in the process becoming the 118th player in major league history to record the milestone. ... The Tigers next have a four-game homestand against Minnesota, a team they are 10-2 against this season.