Mike Zunino, Justin Smoak and Corey Hart all homered for Seattle.
Paxton (1-0) threw 99 pitches in his fifth big league start and struck out nine, including Josh Hamilton all three times he faced him.
Hector Santiago (0-1) was charged with four runs, four hits and three walks in five-plus innings.
Paxton stranded a runner at third base in the first with the help of center fielder Abraham Almonte, who raced in to make a sliding catch on David Freese's sinking liner for the third out. He escaped another jam in the fourth by fanning Hamilton and Howie Kendrick with two men on, then struck out the side in the fifth.
Paxton became the second pitcher in Mariners history to win four of his first five big league starts. The other was Michael Pineda, who did it in 2011. Paxton, a Canadian-born left-hander, was 3-0 with a 1.50 ERA four starts last September.
Hector Santiago (0-1) was charged with four runs, four hits and three walks in five-plus inning after going 2-1 with a 3.63 ERA in five spring training starts. The 26-year-old left-hander, beginning his first full season as a starter, was acquired in December along with Tyler Skaggs from Arizona in a three-way trade with the Chicago White Sox that sent slugger Mark Trumbo to the Diamondbacks.
The Mariners outscored the Angels 26-8 while sweeping a season-opening three-game series for only the second time in their 38-year history. The other time was in 1985, when they started out 6-0 at home against Oakland and Minnesota before losing 12 of their next 13.
It was the first time the Angels were swept in a three-game series to start a season since 1992, by the Chicago White Sox at Anaheim.
Seattle scored 18 of their runs in this series with two outs. Cano, who left the New York Yankees after nine seasons to sign a 10-year, $240 million free agent contract, finished his first series in a Seattle uniform 5 for 11 with two intentional walks.
Santiago walked two of his first three batters and got a visit from pitching coach Mike Butcher before retiring his next seven. But Brad Miller, who homered twice for the Mariners in Tuesday's 8-3 win, legged out a double to right with two outs in the third and came home on Cano's single. Miller drove in the second run with a two-out single in the fifth.
The Mariners broke it open with four runs in the sixth, as Stefan Romero greeted Fernando Salas with an RBI double and Zunino hit his sixth big league homer. Smoak and Hart both homered with two outs in the ninth against Ernesto Frieri.
NOTES: The Angels scored both of their runs in the ninth against Nector Noesi, who gave up Mike Trout's RBI triple and Freese's sacrifice fly. ... Seattle had two players claimed off waivers Wednesday - INF Carlos Friunfel by the Dodgers and LHP Bobby LaFromboise by the Padres. OF Xavier Avery, who was designated for assignment last Friday, cleared waivers and was outrighted to Triple-A Tacoma. ... The Angels claimed RHP Michael Brady off waivers from the Marlins and optioned him to Double-A Arkansas. ... The Angels begin a four-game series Friday night at Houston. The Astros won the season series 10-9 last year, despite finishing a major league-worst and franchise-worst 51-111 after switching over from the NL to the AL. ... Angels pitchers gave up 17 extra-base hits and 15 walks in the series. ... Santiago's only other start at Angel Stadium came with the White Sox on May 18, 2013, when he allowed three runs and four hits over 3 1-2 innings in a no-decision.