Velasquez (2-0) had no walks and extended his scoreless streak to 15 innings with his first shutout in nine career starts. The 23-year-old right-hander, acquired in the trade that sent former closer Ken Giles to Houston, had nine strikeouts in six innings in a 1-0 win at the New York Mets last Saturday.
The Padres were shut out for the fifth time in 10 games. They scored one run - with two outs in the ninth on Wednesday - in the last three games.
Lefty Drew Pomeranz (1-1) tied his career best with eight strikeouts in six innings, allowing three hits and two runs.
Wearing short sleeves on a crisp afternoon, Velasquez blew fastballs past over-matched hitters and kept them off-balance with a biting curve. He struck out the side in the eighth, reaching 97 mph a couple times.
Velasquez retired the last 14 batters he faced. He fanned Wil Myers on a 96 mph fastball to end it, threw both arms up in the air and jumped off the mound.
Howard hit a towering drive out to left-center in the second inning for his third homer. His sacrifice fly made it 2-0 in the sixth.
Padres: They fell to 3-7 with their third loss in a row.
Phillies: Evened their record at 5-5 with their second consecutive series win. First time they're at .500 since they were 3-3 in 2015.
The Padres allowed a routine fly ball drop for the fourth straight game when CF Jon Jay lost Peter Bourjos' popup in the sun and it bounced off his glove. It was scored a double.
Phillies reliever Daniel Stumpf was suspended for 80 games by Major League Baseball after testing positive for a banned performance-enhancing substance. The 25-year-old left-hander has a 40.50 ERA in three appearances.
Phillies: 1B Darin Ruf sat out for the third straight game because of a bruised left rotator cuff.
Phillies: RHP Jeremy Hellickson (1-0, 1.54) takes the mound Friday night in the opener of a three-game series against Washington. Joe Ross (1-0, 1.29) starts for the Nationals.