Robinson Cano hit a two-run double and the Yankees finally quieted Boston's booming bats behind starter Hiroki Kuroda. They took a one-run lead into the ninth inning before Rivera, called on to start the eighth, gave up a wind-aided homer to streaking Will Middlebrooks.
Suzuki hit a one-out single off Workman (5-3) in the bottom half, stole second and advanced to third on Vernon Wells' fly to right.
Workman then fired a high pitch that deflected off the mitt of catcher Jarrod Saltalamacchia and caromed away off the backstop, allowing Suzuki to score easily.
Boston, which began the day with the best record in the majors and an 8 1/2-game cushion in the AL East, had its five-game winning streak snapped. The Red Sox simply outslugged New York in the first three games of the series, giving them a whopping 54 runs, 17 homers and 64 hits during a four-game span that ended Saturday.
Finally on Sunday, some pitching.
After getting big hits from Cano and Mark Reynolds off Boston starter Jon Lester, the Yankees clung to a 3-2 lead through seven innings.
With setup man David Robertson and left-hander Boone Logan sidelined by sore arms, the 43-year-old Rivera (5-2) was brought in to start the eighth for the first time since June 20, 2006, at Philadelphia.
Baseball's career saves leader got through his first inning with little difficulty, but Middlebrooks led off the ninth and lofted high fly to right field. Suzuki initially broke in on the ball, then scurried back as the wind caught hold of it and dropped it a few rows deep beyond the famous short porch at Yankee Stadium.
It was Middlebrooks' fourth home run in five days. Rivera, hands on his hips, stood on the mound with a puzzled, exasperated look on his face and appeared to mouth the word "unbelievable."
He retired the next three batters though, and the Yankees regrouped to finish a 6-4 homestand that keeps them in the wild-card hunt.
Kuroda tossed six gritty innings and left in line for his first win since Aug. 12. Shawn Kelley retired Dustin Pedroia on a grounder with two runners in scoring position to end the seventh.
It was Kelley's first outing since he was roughed up by Baltimore last Sunday. The right-hander had been sidelined because of inflammation in his triceps.
After allowing 34 runs in the first three games of the series, the Yankees appeared to be in trouble again when Kuroda gave up consecutive doubles to David Ortiz and Mike Carp to start the second. But the right-hander fought through a 38-pitch inning and kept the score 1-0 by retiring Daniel Nava on a bases-loaded grounder following a pair of walks.
Kuroda threw 92 pitches in the first four innings and 117 in all. Lester yielded three runs and 10 hits in eight effective innings.
New York tied it in the fourth. Alex Rodriguez singled and scored from first base when Reynolds doubled to deep centre.
Lester ran into some tough luck in the fifth. Chris Stewart blooped a one-out single to snap an 0-for-23 slump before Suzuki and Vernon Wells fisted soft singles that landed just out of the reach of shortstop Stephen Drew.
That loaded the bases for Alfonso Soriano, who struck out. Cano then lined a two-run double over Middlebrooks at third to put the Yankees ahead 3-1.
Ortiz hit a leadoff double in the sixth and scored on Saltalamacchia's RBI groundout.
Stewart, hit by a pitch in the third, was lifted for a pinch-hitter in the sixth with a bruised left foot. He was sent for precautionary X-rays.
NOTES: Boston's last four-game sweep of the Yankees came at Fenway Park in June 1990. The only time the Red Sox have swept a series of at least four games in the Bronx was a five-game whitewash in July 1939. ... Saltalamacchia (back) was back behind the plate after sitting out five games. ... RHP Clay Buchholz is set to rejoin the Red Sox rotation Tuesday night at Tampa Bay after missing three months with a strained neck. ... Yankees LHP CC Sabathia (13-11, 4.86 ERA) starts the opener of a four-game series Monday night in Baltimore against RHP Chris Tillman (15-5, 3.71). ... SS Derek Jeter sat out with soreness in his surgically repaired left ankle. New York manager Joe Girardi said Jeter probably will be held out for a couple of days before further evaluation.