Bay's dinger was preceded by a quick start from the top of the order against Marlins lefty Mark Buehrle. Ronny Cedeno and Justin Turner led off the game with back-to-back doubles, with the latter dropping just fair and out of the reach of Giancarlo Stanton's glove down the right-field line to put two aboard for David Wright. Wright grounded out to score Cedeno for the game's first run.
After Scott Hairston popped out to Jose Reyes in shallow left field, Buehrle walked Ike Davis and hit Kelly Shoppach to load the bases for Bay.
A three-time All-Star, Bay was hitting just .152 entering the day and in the midst of the worst offensive season of his career. He cranked a 1-0 offering from Buehrle to right-center field for his first grand slam since Sept. 8, 2011, when he hit one in the first game of a doubleheader against the Braves.
The homer came in Bay's first at-bat in more than a week. His last plate appearance was Aug. 25 against the Astros.
"I didn't think I was going to hit a grand slam in my first at-bat in a week, but it was definitely nice," Bay said.
It was the Mets' first grand slam since Hairston hit one on June 27 against the Cubs.
While Bay has struggled much of the season, he carried New York to Sunday's win. He added a single in the fourth and finished the day 2-for-4 with four RBIs, marking his fourth multihit game of the season and first since Aug. 16 against the Reds.
"It was one game and it was great to hit that ball, but it's not something that I feel like is out of character, it's just somewhere along the way I lost it," Bay said. "It's been a battle to try to find it and put it all together."
The first was the only inning in which the Mets scored against Buehrle, who finished the day after seven innings of work but saw his three-start win streak come to an end. The early barrage was enough to give righty Chris Young a five-run cushion to work with before he even took the mound at Marlins Park.
"I was just thrilled for [Bay] to come out and hit that ball early through the struggles he's faced and the injuries -- serious injuries, concussions -- it was his win today," Young said. "He set the tone."
Bay set the tone Sunday, but Young maintained it. He shut the Marlins out through the first four innings while holding them to just three hits.
He twice escaped situations with runners in scoring position. With men on second and third in the first inning, Young struck out Stanton and retired Carlos Lee to end the frame. He again got Stanton to strike out in the third with two down and Reyes at second.
Stanton finished the day 0-for-4 with three strikeouts as the Mets snapped the slugger's seven-game hitting streak and generally held him in check all series.
"He's one of the most dangerous hitters in the game," Young said. "He's just so strong and powerful, and you know any mistake can be crushed. You just try to make good pitches to him and hope he doesn't hit it a mile. We did well."
The only blemish on an otherwise solid five-inning outing for Young, who earned his first win in a month, came in the fifth.
He walked Marlins catcher Rob Brantly to start the inning and then gave up a two-out RBI double to Justin Ruggiano to cut the Mets' lead to four. Young limited the damage, retiring Reyes to end the frame and his day on the mound after 94 pitches.
"We couldn't lay off the high fastball with this kid," Marlins manager Ozzie Guillen said. "We kept hitting fly balls, we couldn't make the adjustments. He came out and pitched a good game against us."
Four New York relievers finished off the final four innings as the Mets, who have won seven of eight, secured their first three-game sweep since June 18-20 at home against the Orioles.
"It's important that they keep winning," Collins said. "It's important for them to know they can get the job done."