Mark McAllister found the net twice as Portadown enjoyed a deserved win.
Darren Murray held off the attention of two defenders, turned and smacked the ball into the roof of the net on 47 minutes, before McAllister scored with a classy finish 15 minutes later.
Murray set up McAllister, who found the target with a terrific right-foot finish on 78 minutes to seal victory.
An 84th-minute goal from Jordan Owens was scant consolation for the Crues, who had Paul Heatley sent-off on 57.
The midfielder was shown a red card for swinging an elbow in the direction of Robert Garrett.
Murray twice headed over the bar in the first half, with Gary Breen also unable to find the target with a headed effort.
Murray was also denied by a fine save from Sean O'Neill after the ex-Donegal Celtic striker met Peter McMahon's delivery.
After Murray broke the deadlock, McAllister got on the end of a quick throw-in, shrugged off Davy Magowan and dispatched the ball into the net.
The former Linfield forward added another as he linked up well with strike partner Murray in the absence of Gary Twigg.
For the Ports, it was their first points since their opening day win over Linfield.