The win was their 4th straight as Manitoba swept the two-game series.
Kristian Vesalainen also scored for the Moose.
Mikhail Berdin made 36 saves for Manitoba, who moved to 7-8-0-0.
Landon Bow took the loss for Texas, who lost their ninth in a row.
The Moose got on the board first with a power play marker late in the first period.
Kristian Vesalainen scored with 22 seconds remaining after taking a feed from Sami Niku before stepping into a shot from the top of the left faceoff circle and beating Texas goaltender Landon Bow with a low wrister.
The goal was his 3rd of the season.
Texas drew even at 9:14 of the second when Brian Mclure tipped a Adam Mascherin shot from the right side boards past Berdin to score his 3rd goal of the season.
Emile Poirier restored the Manitoba lead 1:38 later when he shook his check while driving the net hard and snapped a Cole Maier feed past Bow to make it 2-1.
The goal was his 2nd of the season.
There was no scoring in the 3rd period.
SHOTS-TEXAS 37 MANITOBA 16
NOTES-RW Jan Spacek was recalled to the Winnipeg Jets earlier in the day.