Dickey threw a five-hit shutout for his 17th win, Ike Davis backed him with a home run and New York beat Eovaldi and the Miami Marlins 3-0 on Friday night.
Dickey (17-4) is tied with Cincinnati's Johnny Cueto and Washington's Gio Gonzalez for the major league lead in wins.
Eovaldi (4-10) allowed three runs and four hits in seven innings. He walked one and struck out one.
Eovaldi fell to 3-4 with Miami, which acquired the right-hander from the Los Angeles Dodgers in the July 25 trade involving Hanley Ramirez.
"This is the best I've seen him throw since we got him," Marlins manager Ozzie Guillen said. "His control was very good. I was very worried the last three outings. They were very rough. Hopefully with this outing, it will create a little more confidence and he will pitch better the rest of the season."
Davis hit his 25th homer, a two-run shot off Eovaldi in the seventh inning. Davis also had a sacrifice fly in the fourth.
David Wright led off the seventh with a single and Davis followed with a drive into the right-field seats. Davis has hit a league-leading 18 of his home runs this season on the road.
"That was the main one I'd like to have back," Eovaldi said. "I couldn't finish the curveball. I left it right down the middle. He crushed it."
Dickey struck out seven and walked three in his NL-leading fifth
He was especially tough on his fellow All-Star, former teammate Jose Reyes.
Dickey struck out a swinging Reyes with runners on first and second to end the third inning. Dickey picked off the speedy Reyes at first to finish the sixth.
The Marlins put runners at first and second in the eighth, but Reyes grounded out and Carlos Lee flied out.
The game took just 2 hours, 7 minutes.
The Mets won despite getting just four hits. The loss dropped the last-place Marlins three games behind fourth-place New York in the NL East.
NOTES: The series continues Saturday night when Mets RHP Jeremy Hefner (2-5, 4.65 ERA) opposes Marlins RHP Josh Johnson (7-11, 4.00). ... The Mets announced a four-year extension with Double-A affiliate Binghamton of the Eastern League. ... Miami's Donovan Solano (0-for-4) had his 12-game hitting streak snapped. ... It was Miami's fastest home game of the season.