Hooker Jason Macdonald scored late on to give his side a second successive bonus point win.
The Queenslanders appeared competitive for the first half-hour, and closed the gap after half-time.
But the yellow-card loss of David Croft 15 minutes after the break created openings for the Kiwis, which were expertly exploited.
Bancroft opened the scoring with a try after four minutes, although Berrick Barnes closed the gap at the midway point of the opening half with a penalty.
Evans kicked his own three-pointer within seconds, and the half-hour saw Mulipola cross the line.
Former Brisbane Broncos outside half Barnes closed the gap with six minutes of the half to play, claiming a pass from dual international Andrew Walker.
Bancroft replied with a drop goal moments before the break, but Reds captain John Roe put his side back in the game four minutes after half-time with a drive from a line-out.
Evans dispelled thoughts of a comeback with another penalty, and full-back Horton's touchdown wide on the right set up a lead consolidated by the hosts.