"The plan isn't to go out and hit homers. It's a terrible plan," he said, adding, "but tonight it worked out for us."
"There's power in this offense," manager Joe Girardi said. "They can do it, and do it quickly."
The Yankees returned from a 4-6 road trip by beating the Angels for the sixth straight time at home.
Turned around to the right side, the switch-hitting Beltran went the opposite way for his team-leading 14th homer.
"We were feeling good the whole night. That one inning, a couple of homers," Angels star Mike Trout said.
Andrew Miller (3-0) struck out Kole Calhoun, Trout and Albert Pujols in order in the eighth. Aroldis Chapman, who blew a save chance for the first time this season Sunday in Baltimore, quickly returned to form and pitched a perfect ninth for his 10th save.
Shoemaker (3-7) blanked the Yankees on four hits and hadn't even gone to a three-ball count until the sudden power surge in the seventh. 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.
"There's no doubt, he was dominating us," Beltran said.
Pujols blooped an RBI single in the first against Masahiro Tanaka. 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, is three weeks from being able to play in any game, Girardi said.
The Yankees began their eighth annual HOPE Week, honoring individuals and groups for their service and commitment to their communities. Jake Gallin, 14, was saluted for his "Stars for Cars" program, raising about $20,000 by selling magnetic decals in tribute to military veterans. Gardner, McCann, former closer Mariano Rivera and other Yankees surprised Gallin at his hometown in New Rochelle, New York. The teen was on the field for batting practice, joined the exchange of lineup cards and threw out a first ball.
That the tribute came on the 72nd anniversary of the D-Day invasion made it even more memorable for Gallin.
"Good planning," he said.
Two veterans of the D-Day invasion were honored behind home plate before the game. Girardi greeted them, and the men drew applause from both teams as they were driven away on a cart.
Chapman failed to back up the plate after giving up a go-ahead single in the eighth inning of a loss Sunday at Baltimore, and another run scored when the ball got loose. Before Monday's game, Girardi said he planned to deliver a message to Chapman.
"Get your rear end back there," Girardi said. "It will be addressed."
Yankees fill-in first baseman Rob Refsnyder woke up to find that his Twitter account had been hacked. His profile picture was changed, but the hacker didn't make any demands. Refsnyder said he would have some people look into the breach.
Angels: LHP David Huff will come up from Triple-A Salt Lake to start Tuesday night for injury-depleted Los Angeles at Yankee Stadium.
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.
Garcia's 2-run homer in 10th lifts Rangers over Rays 6-4
— Adolis Garcia's first major league homer, a two-run shot in the 10th inning, gave the Texas Rangers a 6-4 victory over the Tampa Bay Rays on Thursday night.
Shaky Royals bullpen hangs on for 7-5 win over Blue Jays
— Jakob Junis ran his consecutive scoreless streak to 14 innings as the Royals staked him to a seven-run lead Thursday night, and a shaky Kansas City bullpen held on after giving most of it back for a 7-5 win over the Toronto Blue Jays.
What goes up must come down ... except this foul ball
Willy Adames skies a foul ball behind the plate, but the ball gets stuck on the catwalk at Tropicana Field.
Guerrero's home run inches Blue Jays closer to Royals
Vladimir Guerrero Jr.'s home run lands a whopping 458 feet out in left-center field as the Blue Jays pull within two runs of the Royals.
Royals jump ahead in first few innings and never look back
The Royals take advantage of an offensive attack in the first four innings and never look back in a win vs. the Blue Jays.
Garcia's first career HR comes at the perfect time for Texas
Adolis Garcia launches a 2-run shot in the 10th inning in the Rangers' win over the Rays.