The Pirates were trailing 3-1 in the bottom of the 13th inning against the Athletics but Pittsburgh reduced the deficit to one on an RBI single by Adam Frazier.
Marte then followed with a three-run walk-off home run to give the Pirates victory.
"Those situations don't happen a lot, but there's something special about them," Marte said after the game. "What I've recognized is that when it comes up to me, it's something about [those situations] that makes me feel big."
Marte came into the game with a .200 average on the season.
"More than anything, all I've got to say is that it signified a lot to be able to be that guy," he said. "It brings me back to that place of being that guy that the team can continue to depend on."
The win moved Pittsburgh to 16-15 for the season, and they now have the best record (21-6) in interleague play since the start of 2018. Meanwhile, the Athletics have dropped eight of their last nine games and fell to 15-21.
Swanson Snaps Seattle's Slump
Seattle Mariners rookie right-handed pitcher Erik Swanson celebrated his first MLB victory in a 10-0 win over the Cleveland Indians. Swanson, who helped snap Seattle's six-game losing streak, threw six scoreless innings and allowed just one hit.
Meanwhile, Derek Dietrich, Jesse Winker and Eugenio Suarez became the first Cincinnati Reds players since at least 1988 to hit three consecutive home runs on three straight pitches.
In other news, Vladimir Guerrero Jr. went 0 for four in the Toronto Blue Jays' 10-2 loss to the Texas Rangers, but he was not the only one having an off game at the plate. Freddy Galvis also went 0 for four, while Brandon Drury and Danny Jansen both went 0 for three.
The San Diego Padres, meanwhile, beat the Los Angeles Dodgers 8-5 thanks to Hunter Renfroe's walk-off grand slam.
And finally, Ben Zobrist had an impressive night on offense and defense for the Chicago Cubs, who crushed the St Louis Cardinals 13-5.
Here's the rest of your full Sunday MLB results:
Atlanta Braves 3-1 Miami Marlins
Detroit Tigers 5-2 Kansas City Royals
Seattle Mariners 10-0 Cleveland Indians
Pittsburgh Pirates 5-3 Oakland Athletics
Philadelphia Phillies 7-1 Washington Nationals
Milwaukee Brewers 3-2 New York Mets
Boston Red Sox 9-2 Chicago White Sox
Texas Rangers 10-2 Toronto Blue Jays
Colorado Rockies 8-7 Arizona Diamondbacks
New York Yankees 4-1 Minnesota Twins
San Diego Padres 8-5 Los Angeles Dodgers
San Francisco Giants 6-5 Cincinnati Reds
Houston Astros 10-4 Los Angeles Angels
Chicago Cubs 13-5 St Louis Cardinals
Baltimore Orioles-Tampa Bay Rays (postponed)
On Tap for Monday: Diamondbacks at Rays
Arizona, who have won four of their last five, will travel to Tampa Bay to begin a three-game interleague series with the Rays. Merrill Kelly (3-2, 3.60) will take the mound for the Diamondbacks while Blake Snell (2-3, 4.31) will start for the Rays.