Kendrick hit two-run homers in the third and fourth, and Pujols lined a three-run shot to left field in the sixth to give the Angels an 11-1 lead.
Jered Weaver (1-2) allowed a run and three hits in six innings. He walked three and struck out three.
The Angels have won 10 straight against the Tigers, the longest active streak in the majors by one team over another.
Smyly allowed four runs and six hits in his first start since 2012. The Angels scored two runs each in the second and third, then broke the game open with four off Putkonen in the fourth.
After excelling in the bullpen in 2013, Smyly is going to start for the Tigers this season, but his first two appearances of the year came in relief because Detroit didn't need a fifth starter yet.
His first chance to start went badly. Smyly needed 82 pitches to get through three innings.
With the Angels already ahead 2-0, Pujols led off the third with a double and Kendrick followed with his first homer of the night. Putkonen came on the following inning and couldn't quiet the Los Angeles bats.
After a two-run double by Trout made it 6-1, Kendrick hit a two-out drive to right-center that was ruled a homer after a review. The ball appeared to glance off a rail above the wall.
Pujols hit his fifth homer of the year to move one swing closer to the 500-homer club. After a disappointing, injury-plagued 2013, the Los Angeles first baseman may be rediscovering his slugging form.
If the Tigers had been able to keep their deficit manageable, their five-run rally in the seventh would have put a lot more pressure on the Angels. Josh Wall, called up from the minors before the game, relieved Weaver in the seventh and allowed five runs on four hits and a walk - without retiring a batter.
Ian Kinsler's two-run single highlighted that rally, but second baseman John McDonald made a spectacular play to retire Victor Martinez, ranging to his left to make a sprawling stop, then rolling and throwing to first from his back. Alex Avila grounded out with runners on second and third to end the inning with the Angels still up by five.
With runners at first and second for Detroit and one out in the ninth, McDonald ended the game with a heads-up play. Don Kelly hit a soft flare toward the second baseman, and with the runners having to freeze, McDonald let the ball drop, tagged second for a force and then ran over and tagged Martinez between second and third for an unassisted double play.
Kinsler had three hits for the Tigers.
NOTES: Detroit RHP Justin Miller, called up before the game, pitched two scoreless innings in his major league debut. ... The Tigers haven't beaten the Angels since Aug. 26, 2012. ... Detroit RHP Max Scherzer (0-1) faces LHP C.J. Wilson (2-1) on Saturday.