Souray opened the scoring 2:35 in and then gave Montreal a 2-1 lead late in the second. He has three two-goal games this season. Seven of his eight goals have come with the man advantage. Montreal captain Saku Koivu recorded his 335th assist with the Canadiens, tying him for 16th on the franchise's career list with Claude Provost.
Vinny Prospal scored for Tampa Bay but Vincent Lecavalier and Martin St. Louis each had 11-game point streaks snapped.
Montreal's Cristobal Huet made 29 saves, including five on Lecavalier in the first. The Canadiens have won five of seven.
Prospal's goal at 7:22 of the second tied it at 1 for the Lightning, 4-1-1 in the past six games.
Souray made it 2-1 from the top of the right circle with 4:48 left in the second. The defenseman had not scored a goal in six games.
Guillaume Latendresse extended the Canadiens' lead to 3-1 on the power play with 10:36 left.
Tampa Bay's Marc Denis made 25 saves.
Notes: The Lightning are 4-6 at home, 5-2-1 on the road. ... Montreal D Mathieu Dandenault returned after missing 12 games with a thigh injury. ... Tampa Bay captain Tim Taylor left after two shifts in the first period with a neck strain. ... Koivu has four assists and six points during a six-game point streak.