Cabrera belted a three-run homer and Raburn chipped in with a bases-clearing double for the Indians, who came into the contest trailing American League wild card-leading Tampa Bay by two games.
Nick Swisher went 2-for-4 with a solo shot and two RBI for the winners, who clinched their three-game series and ran off a fourth straight win overall.
Corey Kluber (8-5) went five innings to get the victory, surrendering two runs on five hits and a walk. He struck out five.
Mets starter Jonathon Niese (6-7) was roughed up for six runs (five earned) on nine hits in a six-inning effort.
Justin Turner went 2-for-4 with two RBI for New York.