Pollard made all six of his first-half shots and Houston led 31-20 despite missing all 10 of its 3-pointers. The Cougars outscored the Colonels 20-5 to open the second half and led by as many as 29.
Damyean Dotson and Danrad Knowles joined Pollard with eight rebounds apiece as the Cougars dominated the boards 53-28 with 18 offensive rebounds leading to 20 second-chance points. Dotson scored 15 points and Rob Gray Jr. 14.
Quinton Thomas scored 15 points off the bench for Nicholls State, which shot just 28 percent.
Houston (10-2) won for the fifth time in six games and begins American Conference play against South Florida on Wednesday.
The Colonels (4-9) lost for the sixth time in seven outings and plays Lamar in its Southland opener on Saturday.