With Chicago trailing 8-7 with two outs and the bases loaded in the seventh inning, Schwindel hit a curveball off reliever Nick Mears to the bleachers in center turn the game around.
Duffy also had three hits and Jason Heyward also went deep as the Cubs won their sixth straight. Duffy had just one homer before Sunday.
Schwindel, who took over at first base in late July after Anthony Rizzo was traded, has gone deep in three straight games and six of seven. It was his first career grand slam and 10th homer with Chicago. He also had a game-winning single in the ninth on Saturday, which gave him some apprehension before Sunday's game.
“I was a little worried because I had to get a new jersey,” Schwindel said. “They tore the jersey off me yesterday.”
Chicago swept the four-game series and has beaten Pittsburgh seven straight.
“It's just about keeping our best foot forward,” Ben Gamel said. “We lost four close games here. We're just gonna keep playing hard.”
Tsutsugo got the homer barrage started with a solo blast in the first to make it 1-0.
Duffy and Heyward led off the second with back-to-back homers to put the Cubs on top.
Reynolds' grand slam — the first of his career — in the third gave Pittsburgh a 5-2 edge, but Chicago answered with five in the bottom half on an RBI single by Ian Happ and Duffy's slam for a 7-5 lead.
Pittsburgh tied it with two runs in the fifth. Jacob Stallings had a sacrifice fly and Gamel, who was hit by a pitch, scored on a wild pitch by Manny Rodriguez with two outs.
The Pirates took advantage of more Cubs miscues in the sixth to take an 8-7 lead. Reynolds singled with one out, Colin Moran followed with a walk and both advanced on a passed ball. Reynolds scored on an infield single by Stallings.
Gamel appeared to save the game for the Pirates in the seventh when he made a diving catch on the warning track in left on a liner by pinch hitter Willson Contreras with runners on first and second for the second out. But Howard walked Rafael Ortega to load the bases and bring Schwindel to the plate.
The rookie slugger said he's just enjoying the moment and not thinking if he's earned a place with the Cubs long term.
“That's the last thing on my mind,” he said. “I'm just gonna show up, have fun and play as hard as I can.”
Schwindel said it wasn't until this weekend that he was recognized walking outside Wrigley Field, but now the fans are trying to settle on a nickname — Frank the Tank or Schwindy City.
Pirates: RHP JT Brubaker and RHP Duane Underwood Jr. were both placed on the 10-day injured list before the game with shoulder inflammation. RHP Kyle Keller and RHP Shea Spitzbarth were recalled from Triple-A Indianapolis.
Cubs: The team said Sunday LHP Brad Wieck is doing well and recovering in Chicago after undergoing a heart procedure on Aug. 31. He has been sidelined since early July with an irregular heartbeat. The 29-year-old underwent a similar procedure during spring training last year. Wieck had a 0.00 ERA in 15 games (17 innings) for Chicago this season. There is no timetable for his return.
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