NEW YORK -- The New York Mets have spent all month searching for a reliable fifth starter and all season hunting for at least one more dependable late-inning reliever. They might have found both Tuesday night.

Jay Bruce capped a marathon by delivering a one-out RBI single in the 12th inning as the Mets edged the Milwaukee Brewers 5-4 at Citi Field.

Bruce's hit -- his first in six at-bats -- made a winner of left-hander Josh Smoker (1-2), who struck out four while throwing three innings for only the second time in 38 major league games.

Smoker entered Tuesday with an 8.00 ERA this season and had produced a scoreless outing in only three of his previous 10 appearances. That stretch was interrupted by a brief demotion to Triple-A Las Vegas in which Smoker worked as a starter in order to better develop his off-speed pitches.

On Tuesday, Smoker might have vaulted himself into consideration for a late-inning role in a beleaguered bullpen (the Mets' relievers entered Tuesday with a 4.85 ERA, the seventh-worst mark in the majors). He wriggled out of a two-on, one-out jam in the 10th, when he struck out the side, before throwing a perfect 11th and a one-hit 12th.

"I think it was really good for me, I think I needed that," said Smoker, who was wearing the crown and boxing robe awarded to the Mets' player of the game following victories. "I've been struggling a little bit of late, so I think as far as getting out there and getting that three innings in, I think it was huge for my confidence and definitely gave me some momentum going forward from here on out."

Smoker's scoreless relief work and Bruce's game-winning hit also ensured the first start of right-hander Tyler Pill's major league career would be noticed. Pill, the third pitcher the Mets have tried in place of injured ace Noah Syndergaard, exited in line for the win after allowing one run on six hits and three walks while striking out four over 5 1/3 innings.

"He lived up to exactly what I heard about," Mets manager Terry Collins said of Pill, who earned the promotion by recording a 1.96 ERA in nine starts between Double-A Binghamton and Triple-A Las Vegas despite throwing a fastball that rarely exceeds 90 mph. "He doesn't give in. He doesn't beat himself."

The previous pitchers to fill Syndergaard's spot, left-hander Tommy Milone and right-hander Rafael Montero, combined to post a 10.61 ERA in five starts in May, which could explain why a dampened crowd of 24,457 gave Pill a warm ovation as he walked off the mound.

"That's a great feeling," said Pill, who turned 27 on Monday. "It's awesome how many people were behind you when you're playing and how much they're rooting for you and cheering for you."

The Mets led 2-1 when Pill left and expanded the lead in the sixth, when Lucas Duda hit a two-run homer.

The Brewers tied the game in the seventh. Domingo Santana drew a bases-loaded walk immediately before Eric Thames and Hernan Perez scored as shortstop Asdrubal Cabrera dropped what should have been the third out, a popup by Jett Bandy. Collins said Cabrera had a hard time finding the ball in a foggy mist that had settled over Citi Field.

"Once we tied it, you think you've got a shot for sure," Brewers manager Craig Counsell said.

The teams traded zeros until the 12th, when T.J. Rivera led off with a pinch-hit single off Wily Peralta (5-4). Michael Conforto drew a walk and was forced at second on Jose Reyes' grounder to first as Rivera moved to third.

Bruce followed by singling on a 2-0 pitch and was engulfed by teammates in between first and second base.

"One of the things you do is when a guy makes an error behind you, you pick him up," Collins said. "It's part of the game and that was a big win for us tonight."

Cabrera had an RBI double in the fifth, when Reyes drew a two-out bases-loaded walk for the Mets (23-27), who have won three straight and four of five.

Travis Shaw had an RBI double in the first for the Brewers (27-25), who stranded 13 runners on base -- including five over the final innings -- in losing for the seventh time in nine games. Orlando Arcia had three hits while Thames, Perez and Shaw each had two hits.

"We got a break, and then we just couldn't cash in on another opportunity at the end there," Counsell said.

Brewers right-hander Zach Davies allowed two runs on six hits and two walks while striking out one over five innings.

NOTES: A pair of Mets recorded milestone hits in the sixth inning, when 2B Neil Walker notched his 1,000th career hit and RHP Fernando Salas, who turned 32 on Tuesday, singled for his first career hit. ... Brewers SS Orlando Arcia extended his hitting streak to a career-high 10 games. ... Milwaukee 1B Eric Thames snapped an 0-for-19 skid with a first-inning single.