Sam Tomkins then broke the Warrington line and Phelps took up the attack from dummy half to claim another, before Paleaasina offloaded to Leuluai, who weaved over to give Wigan a 22-4 interval lead.
In a rare counter attack, Saints pulled a try back on 32 minutes when loose forward Joynt sold a dummy close the Bradford line and stretched out of Nathan McAvoy's tackle to score.