Rodriguez's 660th career homer, a pinch-hit solo blast off Junichi Tazawa, snapped a tie game in the eighth inning and proved to be the difference in the New York Yankees' 3-2 decision over the Boston Red Sox.
The controversial slugger's milestone shot also made a winner of Esmil Rogers (1-1) and lifted the Yankees to an eighth victory in 10 games.
Allen Craig homered for the Red Sox, but the Boston bullpen wasn't able to hold a 2-1 lead after six innings in the opener of this three-game series.
Red Sox starter Justin Masterson departed with the one-run edge and a runner on first after he issued a leadoff walk to Didi Gregorius in the seventh. Tommy Layne came on to retire the next two batters, but hit Mark Teixeira with a pitch and Brian McCann followed with an opposite-field single that brought in Gregorius from second.
After Rogers got David Ortiz to bounce into a double play to end the seventh, Rodriguez drilled a 3-0 fastball from Tazawa (0-1) into the seats behind the Green Monster with one down in the eighth.
It was the first career pinch-hit homer for Rodriguez, and a potentially lucrative one as well. Under the terms of the 10-year contract with the Yankees after he re-signed after the 2007 season, the three-time AL MVP is due to collect a $6 million bonus for reaching Mays' mark.
Previous reports have indicated that the team believes it is no longer liable for the bonus, arguing that Rodriguez breached the terms of the agreement due to his season-long suspension in 2014 for his role in the Biogenesis PED scandal.
Dellin Betances and Andrew Miller protected the lead over the final two innings, with the latter working a 1-2-3 ninth to earn his ninth save.
Both Masterson and New York's CC Sabathia were left with no-decisions after each allowed two runs over six innings of work. The teams stranded seven runners apiece through the first five frames, with the Red Sox owning a 2-1 lead courtesy of Craig's homer in the fourth.
The Yankees touched Masterson for a run in the first when Ellsbury led off with a single and later came around on Beltran's two-out double in the left- center field gap. They failed to capitalize on a second-and-third, one-out situation in the fourth, however, and Masterson got out of a bases-loaded jam an inning later.
Boston pulled even when Xander Bogaerts opened the bottom of the third with a double and took third after Ryan Hanigan ended an 11-pitch battle with Sabathia on a flyout. Bogaerts then narrowly beat Ellsbury's throw home on a shallow fly ball from Mookie Betts to tie the game at 1-1.
Sabathia later benefited from a pair of fortunate bounces to keep New York within one. Hanigan's looper down the left-field line was touched by a fan for a ground-rule double in the fourth inning, preventing Bogaerts from scoring from first and allowing Sabathia to avoid further damage.
He escaped more potential trouble under the same scenario an inning later, as Mike Napoli's shot to right center landed in the bullpen on a hop with Hanley Ramirez trying to come home from first. Pablo Sandoval then grounded out to end the threat.
Sabathia's career-long winless streak was extended to eight starts. He's gone 0-6 with a pair of no-decisions since besting the Red Sox in Fenway Park on April 24, 2014 ... Hanigan exited in the seventh inning after being struck in the wrist by the carom of Layne's pitch that hit Teixeira ... Napoli extended his streak of reaching base against the Yankees to 32 games, the longest active stretch against New York ... Boston had won each of its previous seven series openers this season ... The Yankees have won seven of their last 10 games at Fenway and are now 11-1 when scoring first this season.