Reds suffered their first defeat in six games at the Broadfield after a controversial afternoon at the Broadfield.
Josh Simpson and Hope Akpan were both sent off by referee Darren Deadman to leave the hosts with nine men for the last 19 minutes.
And Pompey made their numerical advantage count when substitute Ashley Harris headed in a cross from Darrel Russell on 74 minutes before Luke Rodgers and Izale McLeod added further goals in the last nine minutes.
Simpson got his marching orders in the 41st minute for his second bookable offence in seven minutes but it was a controversial decision as replays showed that McLeod fell to the ground even though there had been no contact made.
Akpan was shown his second yellow for a foul on the touchline spotted by the assistant, having been booked in the 12th minute for what was the first foul of the game.
There was more drama late on when Pompey midfielder Brian Howard, who had already been booked, brought down Dannie Bulman when he was through on goal but the referee opted to wave play on.
It was a shame for the home fans in a Broadfield record crowd of 5050 but they were still getting behind their side when the game had gone. They must also hope that the old adage that decisions even themselves out over the course of the season comes true.
The atmosphere was superb from the start although both sides struggled to create anything of note in a scrappy opening until Akpan let fly from 25 yards and his shot flew inches wide of Mikkel Andersen's left-hand post midway through the first half.
The game exploded into life on 41 minutes. Keeper Paul Jones' clearance failed to find Mat Sadler and McLeod intercepted and then fell to the ground as Simpson challenged him. Mr Deadman deemed that contact had been made and Reds were down to ten men.
Even with a numerical disadvantage Reds still looked the more composed side as they probed for an opening in the second half with Adams, Nicky Ajose and Gary Alexander all going close.
But 19 minutes from time Akpan was adjudged to have brought down McLeod on the touchline. Mr Deadman took the advice of his assistant before reaching for his top pocket again and Akpan joined Simpson in the dressing room. Both will be banned for next week's trip to Preston North End.
It got worse for Reds on 74 minutes when Lee Williamson stood up an inviting cross to the far post and HARRIS stole in to side-foot past Jones from close range.
Then came another controversial moment as Bulman capitalised on poor defending to race clear but Howard hauled him back. Mr Deadman was in a great position but ruled no contact had been made and waved play on. Howard had already been booked.
Pompey rubbed salt into Crawley wounds with two goals in the last nine minutes. Shaun Cooper brought down McLeod, who was clearly offside, to concede a free kick on the left-hand corner of the box which LukeRODGERS expertly curled into the top corner.
Then McLEOD raced clear of the home defence to round Jones and roll the ball into an empty net.
It completed a tough afternoon for Reds but with a few days this week to regroup they will be anxious to put things right next Saturday when we visit Deepdale to play Preston North End.
Reds: P. Jones, Hunt, Sadler, Cooper, McFadzean; M. Jones (Bulman 57), Simpson, Akpan, Adams; Alexander, Ajose (Connolly 72). Unused subs: Connolly, Clarke, Forte, Walsh, Kuipers.
Attendance: 5050 (1634 Portsmouth)