Murphy's solo shot, on a 2-0 fastball, was the first run Fujikawa (1-1, 6.75 ERA) has allowed since returning from the disabled list on May 10.
"That's one of the bigger home runs I've ever hit," Murphy said, "just because it was a tie ballgame. It was really nice to put a good swing on that ball."
The Mets were able to get big hits when they needed them, whereas the Cubs kept letting scoring opportunities slip away.
Chicago had three leadoff doubles -- including one in the fourth inning by left fielder Ryan Sweeney, who was thrown out on a close play while trying to stretch it into to a triple -- but could not score each time.
The Cubs also had a runner at third with one out in the first and sixth innings, and a man at third with two outs in the fifth.
"We struck out twice with guys on third base and [one out], so those kinds of things come back to haunt you," manager Dale Sveum said.
The Cubs finished 1-for-10 with runners in scoring position.
"Everybody's trying to do his part," said catcher Welington Castillo, who went 2-for-4. "Everybody goes to the plate to do their best and with men on base try to get them in. ... We're trying so hard to do it, but sometimes they make their pitch."
Like New York, Chicago took advantage of the home run and appeared to have the game wrapped up because of it. Mets starter Dillon Gee kept the Cubs off the board until the fifth, when Castillo doubled and Wood launched an offering onto Waveland Avenue to give the Cubs a two-run lead.
It was Wood's fourth career homer and the second time in the past four games a Cubs pitcher has gone deep, following Jeff Samardzija's two-run shot on May 15. Overall, Cubs starting pitchers are hitting .306 with five doubles, two homers and 11 RBIs this month.
"We've got good athletes who can swing the bat, so they're being aggressive up there and taking advantage of the pitchers' mistakes," Sveum said. "It's been a huge bonus."
Sweeney led off the sixth with a homer to right field, his first with the Cubs, to give Chicago a two-run cushion before Lagares tied the score in the seventh with his first Major League homer.
"As soon as it left the hand, I didn't like it," Wood said. "I was hoping he would pop it up or something, but he didn't. He put a good swing on it and hit it out of the park."
Despite that homer -- and a two-out RBI single by David Wright in the sixth -- Wood pitched well, allowing five hits and striking out three. The outing marked his ninth straight quality start, making him the first Cubs pitcher to open a season with that many since Mordecai Brown did so in 1908.
He's also the first Cubs starter to turn in nine consecutive quality starts at any point in a season since 1994, when Steve Trachsel spun off 11 straight from June 5 to Aug. 9, but that was overshadowed by Lagares' homer.
"It was the last batter [Wood] was going to face, and he threw the worst pitch of the game in that situation," Sveum said. "We pitched great. We just couldn't keep the ball in the ballpark."
Despite the loss, the Cubs posted their first .500 homestand since July 27 to Aug. 1 of last season. After an off-day on Monday, they begin a six-game road trip vs. the Pirates and Reds beginning in Pittsburgh, where they hope to connect on the big hits that eluded them on Sunday.
"It's two of the top teams in our division that are playing really well and pitching really well, so it's going to be tough scoring runs," Sveum said. "We've got to do the best we can to take advantage of those opportunities we get. When you're facing good pitching all the time, you better drive in runs when you have the chance, or it's just going to be an uphill battle."