Winning three straight? That's what registered with him.
Junior Lake added a two-run triple in the eighth, and the Cubs came away with their first series sweep since they took three at San Francisco last July 26-28.
"I know we won three games in a row, whether it's a sweep or not," Rizzo said. "It's just nice to win ... especially in a series where we played good baseball."
Wood delivered in a big way at the plate and was in line for the win before New York rallied from a 4-0 deficit.
He hit a two-run homer in the second off Jacob deGrom after Luis Valbuena was ruled safe at home on a sacrifice fly to left following a replay review on what would have been the third out to give Chicago a 3-0 lead. And Wood drove in another run with a fielder's choice grounder in the fourth.
"I feel like we're commanded to hit in this league, so you want to try to be as best as you can," said Wood, who has two homers this season and eight in his career.
The Mets scored two while chasing Wood in the sixth and tied it in the seventh when Brown, who was recalled from Triple-A earlier in the day, connected off Justin Grimm.
Rizzo, however, put the Cubs back on top with a long drive to right-center on a 3-1 pitch for his team-leading 11th homer.
Grimm (2-2) got the win. Pedro Strop stranded two runners in the eighth before Lake made it a three-run game in the bottom half.
Neil Ramirez then converted his first save opportunity, retiring the side in the ninth, and the Cubs swept three from New York at Wrigley Field for the first time since April 2004.
The Mets went 2 for 13 with runners in scoring position and stranded 11 runners after leaving 10 on in each of the previous two games. It added up to a sweep by a team with the worst record in the National League.
"When they all got big league uniforms on, they're major leaguers," New York manager Terry Collins said. "They're trying to beat you just as much as you're trying to beat them. Once in a while they play good, you don't play good, you're gonna get your butt kicked. That's the way it is, that's just the way it is around here."
They wasted several opportunities against Wood, who gave up two runs and five hits in five-plus innings. He tied a season high with five walks but kept pitching out of trouble until the Mets knocked him out in the sixth.
He left with a run in after giving up a leadoff walk to Brown and back-to-back singles by Wilmer Flores and Ruben Tejada. Young added an RBI single off Brian Schlitter with two out, cutting it to 4-2, before Curtis Granderson popped out to end the rally.
DeGrom gave up four runs and five hits over five innings and remained winless in five starts for New York.
The Cubs observed a moment of silence before the game for Don Zimmer, who managed the 1989 team to the NL East crown. Zimmer spent 66 years in pro baseball and was still working as a senior adviser for the Tampa Bay Rays before he died Wednesday at 83. He had been in a Florida rehab center since heart surgery in mid-April. "I lived in St. Petersburg for 12 years, so I saw Don a lot," Collins said. "It's a sad day for baseball. One of the truly iconic baseball personalities in the game. I grew up a Dodgers fan and this guy was one of the great Dodgers. If it wasn't for Pee Wee (Reese) he would have had a tremendous career." ... Mets prized pitching prospect Noah Syndergaard left Thursday's start for Triple-A Las Vegas after experiencing discomfort in his left shoulder following a tag play at the plate. New York said he had precautionary X-rays and the results are pending. It was his first start after returning from the DL because of a mild strain in his right elbow. ... Chicago took Indiana C-OF Kyle Schwarber with the fourth pick in the draft.