New York played the game under protest after beleaguered Boston ace Josh Beckett left with back tightness following Robinson Cano's two-run double in the fifth that made it 5-0.
The Yankees claimed there was no indication of an injury to Beckett to that point, but reliever Manny Delcarmen was given all the time he needed to warm up after the right-hander was removed.
Beckett missed his previous turn in the rotation due to back spasms.
An error by right fielder Marcus Thames, who hit the game-winning homer Monday night off closer Jonathan Papelbon, helped the Red Sox win. Hermida, a defensive replacement, doubled off Rivera (0-1) to snap a 5-all tie. It was the second straight stumble for Rivera after 51 straight saves at home.
Papelbon recovered from Marco Scutaro's error at shortstop on Alex Rodriguez's grounder leading off the ninth to finish with his 10th save after giving up two home runs Monday, a game won by New York 11-9. He gave up a run on Cano's double but then got three tough outs.
He threw up and in on Thames before walking him to put runners on first and third. But he got Juan Miranda to ground out back to the mound and struck out Randy Winn to end it after 4 hours, 9 minutes — the longest nine-inning game in the majors this season, according to STATS LLC.
The start was delayed 59 minutes by rain, and the game was played in chilly, damp conditions on a slick field.
It was a much-needed win for Boston, which at 20-20 is off to its worst start since 1997. The Red Sox improved to 3-5 against New York.
Thames dropped Scutaro's wind-whipped fly to right with one out and one on in the ninth. After an out, J.D. Drew hit a liner over Winn's head in left for the lead. Scutaro also reached on a throwing error by Rodriguez at third to start a four-run rally against Joba Chamberlain in the eighth.
With the Red Sox trailing 5-1 in the eighth, Scutaro, who made two errors at shortstop that led to three runs, reached. Dustin Pedroia singled, Drew hit an RBI double and Kevin Youkilis followed with a two-run double before Chamberlain got an out.
David Ortiz tied it with a drive off the wall in right-center, but paused to admire his shot, thinking it was gone, and was thrown out trying to stretch it to a double by center fielder Brett Gardner's strong throw.
Yankee Stadium was a little more than half full for the start, and the surly crowd that withstood the dreary night as blustery as one of these teams' many October matchups lustily booed Chamberlain as he left the mound having blown a 5-1 lead for CC Sabathia.
Boston's bullpen pitched 4 1/3 innings of relief after Beckett left with two outs in the fifth with tightness in his back.
Daniel Bard (1-1) got one out for the win.
Notes
Yankees RF Nick Swisher took swings off a tee batting left-handed and said he felt great but was out of the lineup for the third straight day with left biceps soreness. He'll take BP Wednesday before the Yankees decide if he'll play against Tampa Bay. … Red Sox manager Terry Francona said OF Mike Cameron (abdomen) did not rejoin the team Monday or Tuesday because his body was sore and it was not injury related. He worked out at Fenway Park. … Yankees DH Nick Johnson had surgery on his right hand.