With the game level at 4-4, Jon Jay hit a grounder to second baseman Dustin Pedroia, who made a fine diving stop to throw out Yadier Molina at home.
Catcher Jarrod Saltalamacchia tried to get Allen Craig at third but his throw was wild. As the ball came in from left field, Craig and Middlebrooks, who was lying on the ground having failed to catch Saltalamacchia's throw, tangled.
Craig stumbled and was tagged by Saltalamacchia, but was awarded home as it was deemed Middlebrooks had obstructed the runner, and the Cardinals won 5-4.
It was the second time in three games the umpires have been in the limelight.
In game one, which Boston won, the crew got together and overturned a poor call made by second base umpire Dana DeMuth, who was at home plate on Saturday's game.
It was a tough loss for Boston who had twice rallied from two runs down.
Matt Holliday and Yadier Molina had RBI hits in the first as Red Sox starter Jake Peavy struggled.
Peavy then loaded the bases with no outs in the fourth, but got three straight outs to get out of the jam, and the Red Sox took advantage with RBIs from Mike Carp and Daniel Nava.
Matt Holliday doubled in a pair in the seventh, but again the Sox fought back with an RBI apiece from Nava and Xander Bogaerts in the eighth, setting up the dramatic finish.
The two teams will go again on Sunday night for game four of the best-of-seven series, again in St Louis.