A slumping Pete Alonso homered and finished with three RBIs and Seth Lugo bounced back from the worst start of his career by tossing 6 1/3 solid innings Tuesday night for the host New York Mets, who kept alive their playoff hopes and delayed the Tampa Bay Rays a chance to clinch a division title with a 5-2 win. The Mets (25-30) began the day three games behind the Philadelphia Phillies in the race for the final National League wild card spot, but the Phillies were swept in a doubleheader by the Washington Nationals before New York’s win was complete. The Rays (36-20) entered Tuesday with a magic number of one for clinching the American League East, but the New York Yankees routed the Toronto Blue Jays 12-1. Lugo (3-3), who gave up four homers and six runs over 1 2/3 innings last Thursday against the Philadelphia Phillies, allowed two runs (one earned) on four hits and one walk while striking out seven. Willy Adames gave the Rays a brief lead in the second by homering off Lugo, but Robinson Cano answered with a solo homer in the bottom half. The blast was the 10th of the year for Cano, who has reached double digits in homers in 16 straight seasons. Alonso, who was mired in a 2-for-34 slump coming in, homered to right off Blake Snell (4-2) in the fourth and added an RBI single off John Curtiss in the sixth. The Rays chased Lugo in the seventh, when Joey Wendle singled with one out and Adames reached on an error by third baseman Todd Frazier. Justin Wilson replaced Lugo, after which Wendle and Adames executed a double steal. Frazier then redeemed himself by fielding a sharp grounder by Kevin Kiermaier and firing home to nab Wendle. Adames raced home on a wild pitch, but Wilson preserved the lead by striking out Hunter Renfroe. Guillermo Heredia homered for his first hit with the Mets in the bottom of the inning and Alonso collected another RBI with a fielder’s choice grounder in the eighth. Chasen Shreve struck out the side in the eighth and Edwin Diaz earned his fifth save with a one-hit ninth. Snell allowed three runs on six hits and three walks while striking out nine over 5 2/3 innings.