There were not an abundance of clear-cut chances at either end, although Matt Tubbs, Matt Clarke and Adam McGurk had the best opportunities for the Blues.
Paul Cook named the same side for the third league match in succession.
There was a familiar face in the opposition line-up with defender Sonny Bradley named Crawley skipper.
Pompey saw plenty of the ball in the early stages – and that was a trend that continued throughout the contest.
But while the visitors were looking composed on the ball, they were struggling to find the right final pass to trouble the Reds.
They did have an opening on nine minutes when a Nigel Atangana pass threaded the opposition defence.
Tubbs raced onto it, but Freddie Woodman came off his line to save and the keeper reacted quickly to gather the loose ball.
Kyle Bennett was next to go close midway through the half, beating his man, cutting into the box and curling a shot narrowly over the crossbar.
The home fans were starting to grow restless as their side kept gifting the ball right back to the Blues.
They did have one opportunity on 33 minutes, but Brian Murphy was able to get behind Luke Rooney’s fierce long-range effort.
The action soon switched to the other end of the pitch and Rooney tugged back the advancing Bennett, earning the game’s first booking from referee Fred Graham.
Joe McNerney then had to race across the box to stop Tubbs from pouncing on a superb incisive pass from Christian Burgess.
And Clarke saw his header cleared off the line by Lee Barnard as Pompey finished the half with a flourish.
Crawley Town 0
Pompey started the second half as they ended the first – on the attack.
The hosts had to deal with a corner in the opening seconds before Woodman did well to gather a dangerous low cross from Roberts.
Cook made an attacking switch on 52 minutes as right-back Ben Davies made way for forward McGurk.
The Blues were still seeing most of the ball, but Crawley came close to snatching a goal on 52 minutes when Gwion Edwards fired into the side netting.
It was still Pompey looking the more threatening, however, and McGurk almost snuck a shot into the bottom corner, only for Woodman to get down and push it clear.
Tubbs did have the ball in the back of the net on 68 minutes, but he was flagged offside after collecting Atangana’s pass.
With the game starting to fall a little flat, Cook made a double substitution as Bennett and Tubbs made way for Conor Chaplin and Jayden Stockley.
That seemed to spark them back into life, although Crawley came close to netting on the break.
The dangerous Lewis Young managed to break free down the right and into the box, but could not beat Murphy at the keeper’s near post.
Pompey continued to push forward in search of a late winner, but the hosts held firm to ensure a share of the spoils.
Crawley (4-1-4-1): Woodman; Donnelly, McNerney, Ashton, Bradley (c); Walton; Young, Rooney (Bawling 77), Smith, Edwards; Barnard (Harrold 64)
Booked: Rooney, Smith
Subs not used: Preston, van den Bogaert, Fenelon, Deacon
Pompey (4-2-3-1): Murphy; Davies (McGurk 52), Burgess, Clarke, Stevens; Atangana, Doyle (c); Evans, Roberts, Bennett (Chaplin 81); Tubbs (Stockley 81)
Subs not used: Jones, Webster, Haunstrup, Hollands
Referee: Fred Graham
Attendance: 4,003 (1,706 Pompey fans)