The veteran first baseman hit the two-run shot in the bottom of the second inning of the victory Thursday in Los Angeles. Pujols' 656th career home run traveled an estimated 375 feet.
"It felt great to give our team an early game," Pujols told reporters. "Thank God for the opportunity to hit the ball out of the ballpark."
Pujols now needs just 28 homers to tie Alex Rodriguez for No. 4 on the all-time list.
Dodgers starter David Price and his counterpart, Diamondbacks starter Merrill Kelly, kept the game scoreless through the first inning.
Price continued to shut down the Diamondbacks in the top of the second inning. Dodgers catcher Will Smith started the bottom of the inning with a single to third base. Kelly then struck out Chris Taylor, which sent Pujols to the plate with one out.
Kelly started that exchange with a 91.7-mph sinker for a called strike. He then tossed in a 90.9-mph cutter. Pujols smacked the pitch over the right-field fence to give the Dodgers a 2-0 lead. The blast left Pujols' bat at 99 mph, according to Statcast.
Diamondbacks third baseman Eduardo Escobar hit a 395-foot, two-run homer to tie the score at 2-2 in the top of the sixth inning.
Smith returned to the plate for a go-ahead homer for the Dodgers in the bottom of the next inning. The Dodgers catcher led off the bottom of the seventh frame. He hit the first pitch he saw from Kelly to left field for a 371-foot solo shot.
Dodgers closer Kenley Jansen pitched a no-hit ninth inning to earn his 10th save of the season. Price allowed three hits in two scoreless innings, but did not receive a decision for the effort. Kelly allowed six hits and three runs and threw 12 strikeouts in seven innings. He dropped to 2-5 this season.
Pujols went 1 for 3 with two RBIs, a run scored and a strikeout in the win. He is hitting .273 through four games with the Dodgers. Smith went 2 for 3 with two runs scored and an RBI in the win. Dodgers infielder Max Muncy went 3 for 4 in the win.
The Dodgers (26-18) face the San Francisco Giants (28-16) at 9:45 p.m. EDT Friday at Oracle Park in San Francisco.