Will Middlebrooks’ slump finally died last night. It happened at about 10:30 p.m., so you probably missed it, considering the Bruins were thundering away in overtime back home. But down to his last strike, and with the Red Sox trailing by two runs with two outs in the ninth inning, Middlebrooks lined a changeup from Tampa Bay closer Fernando Rodney into left-center field for a three-run double. The short-term consequence: A come-from-behind 4-3 victory, the Red Sox’ first when trailing after eight innings, in the finale of a three-game series against an American League East rival. But it meant so much more. “I think it can have a carryover,” manager John Farrell said after the Sox won their second consecutive game and for only the fourth time in 13 games. “We’ve come through a pretty tough 10-day stretch. Even though we were going up against a guy (Rodney) who’s got tremendous stuff, there was no give-up, there was no letdown.” And it was Middlebrooks, tortured for the past six weeks, who delivered the big hit. The past few days had built to this moment. Even after a May 7 collision with teammate David Ross left his ribs bruised and sore, he collected five doubles in a three-game span last weekend, waged a 10-pitch at-bat with tough Rays reliever Jake McGee three nights ago, then doubled and homered to right field Wednesday night. All positive signs to be sure. But a two-strike, game-winning blow against hard-throwing Rodney? That was the ultimate catharsis.