Alan Anderson scored a team-high 24 points while DeMar DeRozan added 19 to lead a spirited Toronto effort that handed the Rockets a seventh straight road loss.
"We've been working so hard, we've been practising so hard and we were staying together and trying to do a lot of things," Raptors guard Jose Calderon, who had 18 points, 14 assists and 10 rebounds for a triple-double, said.
"I know it's been a tough time and we couldn't turn that into a win (earlier) but it feels great."
Playing without injured Andrea Bargnani and Kyle Lowry, two of the Raptors' top three scorers, Toronto built an early 12-point lead and held off a late Houston charge for its first win streak since April of the 2011-12 season.
Houston pulled to within two points twice during the final minute but Anderson helped put the game out of reach with a reverse lay-up with 11 seconds left in regulation.