Norris, ranked No. 99 on MLBPipeline.com's Top 100 Prospects list, scattered four hits and one walk. He hasn't allowed a run in five of his 10 starts this season.
Norris' 0.72 ERA is the lowest in the Florida State League and second best in the Minor Leagues among pitchers who have thrown at least 33 innings. He has struck out 60 batters and walked 14 in 50 1/3 innings.
Outfielder Dalton Pompey, the Blue Jays' No. 19 prospect, went 2-for-5 with a run scored on Tuesday. He extended his hitting streak to nine games and is hitting .333 in 46 games this season.
Teddy Cahill is a reporter for MLB.com. Follow him on Twitter at @tedcahill. This story was not subject to the approval of Major League Baseball or its clubs.