They recovered from a disastrous start that saw James Coppinger score and Anton Walkes grabbed a deserved equaliser.
The hosts dominated from that point on, only for John Marquis to leave them trailing once more after the break.
But Brett Pitman came off the bench to level and the Blues saw out a nervy conclusion that saw Kal Naismith go in goal following an injury to Stephen Henderson, before Christian Burgess was sent off.
Kenny Jackett made four changes from the side narrowly beaten at home by Shrewsbury the previous week.
New signings Henderson and Walkes were both handed debuts, with there were also starts for Matty Kennedy and Connor Ronan.
That meant Luke McGee, Jamal Lowe and Naismith all dropped to the bench, while Adam May was serving a suspension.
But Henderson’s first job was to pick the ball out of his own net, as – for the second time this season against Doncaster – Pompey made a terrible start.
Walkes blocked Alfie Beestin’s path to goal, but Coppinger picked up the loose ball and managed to force the ball home.
It might have got even worse for the hosts, as they struggled to keep hold of the ball in the opening stages.
The evergreen Coppinger was proving a nuisance and one shot was dealt with by Henderson, while another was deflected just past the post.
Rovers did have the ball in the net again on 16 minutes when former Fratton loanee Marquis stooped to convert Coppinger’s cross, but their celebrations were cut short by the linesman’s flag.
Pompey suddenly found their feet, though, and proceeded to dominate the remainder of the first half.
Burgess was not quite able to take advantage when Ben Close’s free-kick was helped on, first by Matt Clarke and then Oli Hawkins.
But a leveller did arrive on 19 minutes and it was WALKES who was able to celebrate a goal on his Blues bow.
A corner was sent into the box by skipper Gareth Evans and that led to a scramble in the visitors’ box.
Clarke and Walkes both tried to stab home the loose ball, although it was the latter who got the vital touch before wheeling away to celebrate.
Pompey did not stop there, though, and a shot from Evans was deflected behind, while Tyler Garratt did well to beat Hawkins to Kennedy’s cross.
Ian Lawlor then made a stunning save to keep out Clarke’s header from point-blank range when the centre-back met Dion Donohue’s excellent corner.
There were plenty more dangerous deliveries into the Doncaster box – particularly from Kennedy – although the visitors were defending firm.
But there was late drama at the other end just before the break, as a late challenge from Donohue led to a melee.
Referee Graham Salisbury calmed things down, though, showing yellow cards to the initial perpetrator, as well as Burgess and Marquis.
Doncaster Rovers 1
It was still the hosts on top once the action restarted, although clear-cut opportunities were at a premium.
Hawkins met a low cross from Kennedy, only for a well-placed Andy Boyle to make a vital block in the Doncaster box.
Pompey almost took the lead just before the hour mark, though, as Ronan sent Close through on goal, only for Lawlor to tear from his line and make another fine save.
Jackett soon made his first change of the afternoon, as Hawkins was withdrawn for top scorer Pitman.
But the Blues then undid all their good work by leaving Marquis in acres of space to head home Coppinger’s corner and restore Rovers’ advantage.
The hosts tried to battle back, but some wayward crossing was undoing their progress into promising areas.
A double substitution was made to reinvigorate Pompey on 72 minutes, with Kennedy and Evans withdrawn for Naismith and Lowe.
Naismith almost levelled when he tried to sneak a long-range shot inside Lawlor’s near post, only for the keeper to get down and save.
But Pompey did find another equaliser from Donohue’s resulting corner, as PITMAN managed to bundle the ball over the line.
Delight turned to concern soon after, though, as Henderson went down off the ball and – clearly distraught – had to limp off.
Jackett had already made all three of his allowed changes, meaning Naismith had to don the gloves for the closing stages.
The challenge became even harder early in the seven minutes of stoppage-time, when Burgess handled and was shown a second booking to leave the Blues with nine men.
Naismith came to the rescue, though, making a key save with his feet to deny Ben Whiteman and ensure Pompey secured a point.
Pompey (4-2-3-1): Henderson; Walkes, Burgess, Clarke, Donohue; Thompson, Close; Evans (c) (Lowe 72), Ronan, Kennedy (Naismith 72); Hawkins (Pitman 59)
Goals: Walkes 19, Pitman 81
Sent off: Burgess (two yellow cards)
Subs not used: McGee, Deslandes, Widdrington, Chaplin
Doncaster (4-1-2-1-2): Lawlor; Blair, Anderson, Boyle, Garratt (McCullough 59); Houghton; Whiteman, Rowe; Coppinger (c) (Kongolo 73); Beestin (Kiwomya 59), Marquis
Goals: Coppinger 4, Marquis 63
Booked: Marquis, Anderson
Subs not used: Marosi, Alcock, Mason, May
Referee: Graham Salisbury
Attendance: 17,364 (366 away fans)