Drame shot 10 of 14 from the field to score 23 points and pulled down a dozen rebounds as the Bobcats pulled away in the second half, leading by as many as 19 points midway through the period.
Quinnipiac (17-8, 12-4), winners in six of its last seven games, now is in a three-way tie for second place in the Metro Atlantic Conference with Manhattan and Canisius, all two games behind conference-leading Iona.
Ike Azotam scored 16 points and pulled down 11 rebounds for Quinnipiac, which shot 50 percent from the field (29 of 58) and outrebounded the Peacocks 42-28.
St. Peter's (9-16, 5-11) was led by Trevis Wyche and Marvin Dominique, who scored 16 and 15 points, respectively. Chris Burke added 12 points.