His second comes against the San Diego Padres, who have played well of late but will now be without their lone All-Star.
Norris takes the mound as Baltimore begins an eight-game trip Tuesday night in San Diego, which will be without Everth Cabrera.
Cabrera was one of 13 players punished Monday for connection to the Biogenesis clinic and accepted a 50-game suspension. The 26-year-old shortstop, hitting .283 in 95 games for the Padres, ranks second in baseball with 37 steals and leads San Diego with 54 runs.
The Padres (52-60) have won 10 of 15 but are 5-12 without Cabrera, who was 2 for 5 with two RBIs in Sunday's 6-3 home win over the New York Yankees.
Devoid of their leadoff hitter - who was 5 for 10 as San Diego swept a two-game set in Baltimore on May 14 and 15 - the Padres will try to knock off Norris (7-9, 3.89 ERA), who enjoyed a strong debut with Baltimore in a 6-3 win over Houston on Thursday.
The right-hander, acquired from the Astros a day earlier, limited his old club to four hits and two runs - both on homers - over six innings while striking out a season-high eight. He was rewarded with a shaving-cream pie to the face during a post-game interview.
"He was good," catcher Matt Wieters said. "He was able to locate his fastball both in and out and mix in his off-speed, throw his slider behind in the count."
Norris also enjoyed five runs of support - something he had received just once in 21 starts with Houston. The Astros had given him three runs of support or fewer 18 times.
The Orioles (61-51), however, were 0 for 11 with runners in scoring position in a 3-2 loss to Seattle on Sunday. Danny Valencia homered in his first game since being recalled from Triple-A Norfolk for his third stint with Baltimore, but Henry Blanco hit a go-ahead home run in the seventh.
San Diego, which has held opponents to three runs or fewer in 12 of 15, will give the ball to Edinson Volquez (8-8, 5.56). Volquez has been slightly better in three starts since the All-Star break with a 2-0 record and 4.32 ERA but remains among baseball's leaders in walks per nine innings with 4.3.
He issued five walks while allowing two runs and four hits over 6 1-3 innings of San Diego's 4-2 win over Cincinnati last Tuesday. However, Baltimore is one of the majors' least patient teams, walking once every 15.8 plate appearances and striking out every 5.5.
Norris, who is 2-1 with a 3.13 ERA in four career starts versus San Diego, has never faced Carlos Quentin, who could return to the Padres' lineup Tuesday according to the team's official website. Quentin, tied for the team lead with 13 home runs, hasn't played since leaving last Tuesday's game with a sore right knee.
Chase Headley is 3 for 9 off Norris with a home run and owns an .880 OPS in 16 games since the All-Star break compared to a .720 mark on the season.
Chris Davis, whose 40 homers lead the majors, doubled twice in seven at-bats in the teams' first two meetings.