The Red Sox were four runs behind in the eighth and still 5-2 down heading into the bottom of the ninth, but they stayed alive with a series of gritty at-bats against Indians closer Chris Perez.
The inning began with a walk for Dustin Pedroia and included RBI ground-outs from Mike Napoli and Jarrod Saltalamacchia, as well as stolen bases from David Ortiz and Stephen Drew, before Ellsbury drove in two off Joe Smith's first pitch after Perez had to leave the game with an injury.
It was Boston's second comeback win in as many days and it was matched by the Toronto Blue Jays, who also had a four-run ninth to walk off with a 6-5 win over the Baltimore Orioles on Munenori Kawasaki's ninth-inning double.
Matt Wieters' two-RBI double in the top of the ninth put Baltimore 5-2 up, but JP Arencibia drove in Edwin Encarnacion to begin the rally.
Adam Lind then scored on a Mark DeRosa force-out, before Kawasaki doubled to score Arencibia and DeRosa and give the Blue Jays a memorable win.
Josh Hamilton's eighth home run of the season began the Los Angeles Angels' rally in the seventh as they stretched their winning streak to eight by beating the Kansas City Royals 5-2.
The Angels belatedly caught fire after Wade Davis had held them scoreless through six, with JB Shuck driving in a pair on three hits.
Stephen Strasburg hurled eight innings of one-run ball as the Washington Nationals beat the Philadelphia Phillies 6-1.
Strasburg scattered five hits and fanned nine, his only run allowed coming via a balk in the eighth, while Steve Lombardozzi drove in a pair.
Alex Cobb took a shutout into the ninth as the Tampa Bay Rays beat the New York Yankees 8-3.
Brett Gardner got the Yankees on the board by homering in the ninth, but it was still an excellent outing for Cobb who in the end surrendered two runs on five hits in 8 1/3 innings, striking out eight.
The Seattle Mariners claimed their first win in nine as Jason Bay's ninth-inning RBI single lifted them to a 4-3 victory over the Texas Rangers.
Bartolo Colon fanned nine in seven scoreless innings to lift the Oakland Athletics to a 6-2 victory over the Houston Astros.
Welington Castillo drove in the winning run in the 10th as the Chicago Cubs rallied from an early four-run deficit to beat the Cininnati Reds 5-4.
Avisail Garcia fired a bases-clearing triple to lift the Detroit Tigers to a 6-1 win over the Minnesota Twins, the Arizona Diamondbacks overcame the San Diego Padres 6-5 and the St Louis Cardinals were 5-3 winners over the Los Angeles Dodgers.
The Chicago White Sox beat the Miami Marlins 5-3, the New York Mets saw off the Atlanta Braves 4-2, the Pittsburgh Pirates edged out the Milwaukee Brewers 5-4 and the San Francisco Giants eased past the Colorado Rockies 7-3.