A couple of loanees ensured they had a two-goal advantage at the break, with Matt Clarke heading the opener before Marc McNulty doubled the advantage.
The Blues dominated for most of the afternoon and got a deserved third when Gary Roberts found the target following excellent work from fellow substitute Ben Tollitt.
Paul Cook made one change from the side that drew with Luton five days earlier.
Adam Webster returned from suspension to take his place in the centre of defence, with Adam Barton dropping to the bench.
Before kick-off there was a minute’s applause in memory of former Pompey keeper Pavel Srnicek, who sadly passed away before Christmas at the age of just 47.
There were a couple of familiar faces in the opposition line-up, with Darryl Flahavan and Sonny Bradley both starting for the Reds.
The hosts made a bright start and Caolan Lavery could not quite guide Ben Davies’ cross on target with a diving header.
Enda Stevens then delivered a dangerous low centre from the left that Bradley was forced to clear behind.
And the Blues broke the deadlock from the resulting corner, with CLARKE rising highest in the box to guide home Davies’ cross on 13 minutes.
McNulty tried to double the advantage moments later, but sent an angled effort whizzing past the post.
Pompey were totally on top and Kyle Bennett saw his strike blocked after meeting Lavery’s cut-back, while Danny Hollands blazed the loose ball over.
Clarke then met another corner from Davies, although this time his radar was off and the ball flew wide.
Lavery thought he should have been awarded a penalty midway through the first half after tangling with Lewis Young, but referee Dean Whitestone was not quite so convinced.
Stevens was providing a real threat down the left and twice saw low crosses somehow evade his team-mates.
But it proved to be third time lucky on 26 minutes when the left-back picked out McNULTY, who took a touch before sliding the ball past Flahavan.
Crawley were struggling to keep the Blues at bay and it took brave blocks from Young and Bradley to keep out goal-bound efforts from McNulty and Bennett respectively.
The visitors finally carved out an opening on 39 minutes, but after beating Clarke, Roarie Deacon hit his shot straight at Brian Murphy.
Bennett then made a vital challenge to dispossess Luke Rooney on the edge of the box, while Simon Walton hit a long-range free-kick safely into Murphy’s arms.
But most of the action was still happening at the other end of the pitch and Flahavan did well to keep out a strike from Bennett that took a heavy deflection off Jon Ashton.
Then, in stoppage-time, an unmarked Gareth Evans somehow failed to connect with Davies’ cross from just a few yards out.
Crawley Town 0
Pompey picked up where they left off at the start of the second half and Stevens drilled a low shot narrowly wide.
Bennett was next to go close, cutting inside and sending a fierce effort fizzing inches over from the edge of the box.
But the visitors came close to reducing the deficit just past the hour mark, when Davies conceded a free-kick that Gwion Edwards curled against the crossbar.
Crawley were then thankful to Young, who prevented them from falling further behind when he cleared Lavery’s bullet header off the line.
Cook made a double substitution on 67 minutes, with McNulty and Evans making way for Roberts and Tollitt.
Lavery then had a chance to extend the hosts’ advantage when he met a cross from Tollitt, only to send his header sneaking past the far post.
Pompey were not having much to deal with at the other end, although Matt Harrold should at least have found the target when he collected Young’s pass.
And the hosts wrapped up a comfortable victory on 83 minutes after their two substitutes combined to devastating effect.
Tollitt picked the ball up from a Crawley corner and surged almost the full length of the pitch before teeing-up ROBERTS for a cool finish.
Pompey (4-2-3-1): Murphy; Davies, Webster, Clarke, Stevens; Hollands, Doyle (c); Evans (Tollitt 67), McNulty (Roberts 67), Bennett; Lavery (Chaplin 85)
Goals: Clarke 13, McNulty 26, Roberts 83
Subs not used: Bass, Barton, Atangana, McGurk
Crawley (4-1-4-1): Flahavan; Young, Yorwerth (Ashton 23), Bradley (c), Hancox; Walton; Deacon, Rooney (Tomlin 77), Smith (Emmanuel 46), Edwards; Harrold
Subs not used: Preston, Bawling, Jenkins, Fenelon
Referee: Dean Whitestone
Attendance: 16,606 (567 away fans)