Parker scored 34 points and handed out 13 assists, hitting all 12 of his attempts from the foul line.
The last five victories in San Antonio's streak have come at the start of a nine-game road trip that will take the Spurs across the country next for meetings with the Los Angeles Clippers, Utah, Portland and Denver.
During the current winning stretch, Parker has popped up with game-saving performances. He scored 42 points against Oklahoma City Feb. 4 and 37 against Philadelphia Feb. 8. San Antonio last lost Jan. 29 against Dallas.
San Antonio had an eight-point lead after one quarter and spent the rest of the game holding off the Raptors. The Spurs' advantage going into the fourth quarter was only five and Toronto closed within a point with 4:24 to go before San Antonio went on a game-closing 16-10 run.
Tiago Splitter and Danny Green both added 13 points for the Spurs. DeMar DeRozan had 29 for Toronto.
Both sides shot 54 percent from the field, but San Antonio went 23-of-25 from the foul line while the Raptors made just 9-of-14.