Parris (1-2) walked two and struck out four, earning his first win since July 4, 2001. Since coming off the disabled list on June 16, he had allowed 11 runs and 25 hits in 11 2/3 innings prior to Saturday's outing.
The Blue Jays roughed up Andy Pettitte (2-3) for six runs and 10 hits in just 3 1/3 innings.
The loss ended a five-game winning streak for the Yankees and dropped them to 6-2 on a nine-game homestand.
Pettitte has been ineffective in three of four starts since coming off the disabled list. He tossed a three-hit shutout against the New York Mets on Sunday for his first win since April 5 but took a step back against Toronto.
After breezing through the first two innings, Pettitte was tagged for five runs and six hits in the third, then was lifted after giving up a sacrifice fly to Joe Lawrence in the fourth.
Rookie Ken Huckaby hit his first major league home run, a two-run shot off Brandon Knight in the fifth that made it 8-0. Huckaby came into the game with just six RBI.
The Yankees avoided the shutout with three runs in the ninth off Scott Cassidy, two coming on pinch hitter Chris Widger's bases-loaded single.
Through eight innings, the Yankees were none for 11 with runners on base and got just one man past second base against Parris. That was Nick Johnson, who advanced in the third on a wild pitch.
Jackson was honored as part of the Yankees' annual Old Timers' Day celebration.
Celebrity Couples of 2014 [PHOTOS]