The Yankees returned from a 4-6 road trip by beating the Angels for the sixth straight time at home.
Beltran was the first batter Jose Alvarez faced after relieving starter Matt Shoemaker. Two-out singles by Jacoby Ellsbury and Brett Gardner prompted the Angels to go to their bullpen, and Beltran struck for his 14th homer.
Andrew Miller (3-0) struck out Kole Calhoun, Mike Trout and Albert Pujols in order in the eighth. Chapman, who blew a save chance for the first time this season Sunday in Baltimore, pitched a perfect ninth for his 10th save.
Brian McCann and Starlin Castro hit back-to-back home runs with two outs in the Yankees seventh, tying it at 2. Shoemaker (3-7) slapped his hands together while he walked to the dugout when the inning ended.
Shoemaker blanked the Yankees on four hits and hadn't even gone to a three-ball count until the sudden power surge. McCann hooked a long drive just foul on a 3-2 pitch, then hit the next delivery into the second deck.
Two pitches later, Castro connected for the Yankees' fourth set of consecutive home runs this season.
Shoemaker stuck out six, and has fanned 39 without a walk in five starts.
Pujols blooped an RBI single in the first against Masahiro Tanaka. Kole Calhoun added a sacrifice fly in the third for a 2-0 lead.
Both the Angels and Yankees began the day 26-30. For teams often in the playoffs, this was the latest they'd met in a season with below-.500 records since August 1992.
The Yankees played at home for the first time since the death of Muhammad Ali. They held a pregame moment of silence for the boxing great, who beat Ken Norton at the old Yankee Stadium in 1976.
Angels: Setup man Joe Smith has been nursing a sore hamstring, and manager Mike Scioscia said the team would wait to see how the righty feels later in the day before deciding whether to put him on the disabled list. SS Andrelton Simmons was set to begin a minor league rehab assignment at Class A. He's been out since May 9 after having thumb surgery.
Yankees: 1B Mark Teixeira, already on the 15-day disabled list with a tear in his right knee, was supposed to see a doctor at the ballpark.
Angels: LHP David Huff will come up from Triple-A Salt Lake to start Tuesday night for injury-depleted Los Angeles at Yankee Stadium. He's 25-28 in seven seasons with Cleveland, the Yankees, Giants and Dodgers. He was in the minors with Kansas City earlier this year, and is 0-1 with a 5.40 ERA in three starts for Salt Lake. Yankees: Michael Pineda (2-6, 6.41 ERA) has been struggling to stay in the rotation. He pitched well in his last start, striking out eight and walking none in a no-decision at Detroit.