Davis and Murphy both finished 3-for-5 with four RBIs and three extra-base hits.
"I don't want to hit .200 for the year," Davis said. "It's a step in the right direction from whatever I was at for a long time."
Davis raised his batting average from .192 to .201 on Wednesday, reaching the .200 mark for the first time this season.
"He's hit the ball very well, especially in the last 10 games," manager Terry Collins said. "He certainly feels better about himself."
Davis added a three-run home run, Scott Hairston blasted a grand slam, David Wright knocked in four runs on two hits and Murphy launched his second home run of the game for the first multi-home run performance of his career all in the fifth and sixth innings alone.
Murphy's two-run homer and solo shot, combined with Hairston's grand slam and Davis' three-run blast, completed the home run cycle for the Mets -- at least one of each type of home run.
Murphy, Davis, Wright and Hairston knocked in all 17 of the Mets' runs, each providing at least four RBIs.
"We haven't had a lot of days where we've had multiple guys in the lineup come up big," Collins said. "We kind of thought going into Spring Training we'd have more of those. I'm hoping that's something that continues."
The Mets, who totaled four runs through the first two games of the series, left just two batters on base through six innings Wednesday. They left 12 runners on base in Tuesday's 5-3 defeat.
Murphy and Davis combined for five extra-base hits in their first three at-bats, while Wright totaled five RBIs in his first four at-bats.
Murphy said he was much more excited about his first home run with two outs in a 2-1 game than his second home run with the Mets leading 8-1 at the time.
"Today, I just tried to relax and hit the ball hard," Murphy said. "The fact the wind was blowing out didn't hurt."
Six Mets runs crossed the plate in the fifth and sixth innings. Right fielder Lucas Duda walked in the fourth, fifth and sixth innings, scoring on each occasion. After a baserunning blunder Tuesday, Duda held up again after a Davis double in the fourth inning, but had enough time to score the first of three runs in the frame.
Starter Jonathon Niese (6-3) went seven innings to earn the win after being handed a 15-run cushion. He is 4-1 with a 2.35 ERA and five quality starts in his last seven starts.
"He had a real good cutter today," Cubs outfielder Joe Mather said. "His cutter dominated the game. He was throwing it in on righties and away from lefties."
Niese is 4-0 with a 1.89 ERA in eight daytime starts this season. The Mets are now 19-10 during day games, in which Wright is hitting .408 this season.
Niese put runners on the corners to begin the game, before picking off Starlin Castro at first base and holding Mather at third to keep the Cubs off the board in the first.
"I really wanted just to keep him close, that way he didn't get a good jump for a double-play ball," Niese said. "I was fortunate I picked him off."
Niese put two runners on base in the first, second and third innings, but held the Cubs to one run in that span on an RBI double by third baseman Luis Valbuena.
"You could tell before the game he had that edge to him today," Collins said. "I was very happy. I knew he'd go out and pitch well. In the second inning, he was furious that he gave up the run."
Niese even helped himself out at the plate, drawing walks and scoring in the fifth and sixth innings. Niese's strikeout in his second at-bat of the sixth inning marked the 25th plate appearance by the Mets between the fourth and sixth innings.
"I think the offense did more than anything," Niese said. "Obviously, scoring 17 runs, that just makes the pitcher's job a lot more easier."
The Mets hadn't scored more than 11 runs in a game this season and hadn't scored more than six runs since a 9-6 win on June 14 against the Rays.