Duda went 2-for-4 with a three-run home run off Anthony DeSclafani in the third inning and another three-run home run off Tony Cingrani in the seventh inning that gave the Mets a 9-0 lead.
Syndergaard (9-7) struck out 11 batters in 7 2/3 innings for the Mets (87-67), who took an 8 1/2-game lead in the NL East over the Nationals, who lost 8-2 to the Phillies on Friday.
The Mets' rookie pitcher cruised, retiring 16 straight batters before allowing Brennan Boesch's solo home run with two outs in the bottom of the eighth inning to end the shutout. He struck out at least two batters in five innings.
Curtis Granderson was one of seven Mets who had multi-hit games, going 2-for-5 with four RBIs. Syndergaard also went 2-for-3 with an RBI single in the second inning that gave the Mets a 1-0 lead.
Duda's first three-run home run gave the Mets a 4-0 lead in the third inning, and his second one came in a five-run seventh inning.
Granderson hit an RBI double to make it 5-0 and David Wright and Daniel Murphy hit back-to-back singles to make it 6-0. Duda then crushed a 3-1 fastball off Cingrani to blow the game wide open.
In the eighth inning, Granderson hit a three-run home run off J.J. Hoover to make it 12-0.
The Mets' bullpen allowed six hits and three runs in 1 1/3 innings.
DeSclafani (9-12) allowed seven runs (five earned) and nine hits in 6 1/3 innings for the Reds (63-90).
The Mets and Reds play the third game of a four-game series Saturday at 4:10 p.m.
Matt Harvey (12-7, 2.80 ERA) will pitch for the Mets and face Cincinnati's John Lamb (1-3, 4.60 ERA).
Matthew Cerrone, MetsBlog.com
Well, this it... The Mets are one win, or one Nationals loss, away from winning the NL Eastern Division, either of which could occur Saturday night...
Tonight, Syndergaard was as dominant as we've ever seen him. And, as Gary Cohen suggested during the broadcast, he has to be a consideration for more than one start in what is likely to be an NLDS matchup against the Dodgers. At the same time, Duda continued his recent turnaround to create half the team's offense on the night.
Tomorrow will be a waste of a day, as I'll only be watching the clock and waiting for game time. Have a nice night, gentlemen. It's shaping up to be a memorable weekend.