Ben Marshall rescued a point for ten-man Rovers with a stunning injury-time free kick.
The Rovers midfielder bagged his fourth goal of the campaign with a 93rd minute equaliser to earn a share of the spoils.
Gary Bowyer's side had the better of a tight first half, Jordan Rhodes and Shane Duffy both missed in front of goal before Rudy Gestede was denied by a strong save from Dean Gerken.
However Ipswich started the second half strongly but Matt Kilgallon was perhaps unfortunate to see red when he appeared to be fouled by Conor Sammon.
David McGoldrick took full advantage as he bent his free-kick into the back of the net to leave Rovers with a mountain to climb.
As the home side looked to press home their advantage McGoldrick hit a post, whilst Stephen Hunt was denied by a clearance off the line by Duffy, before the Irishman played a key role in clinching a point for the visitors.
As Duffy was felled by Christophe Berra just outside the box deep into injury-time, Marshall took the honours from 20-yards, and how.
Rovers made three changes from the side that drew with Huddersfield Town a fortnight ago.
With Grant Hanley and Josh King picking up injuries on international duty, their places were taken by Matt Kilgallon and the returning Rudy Gestede.
Ryan Tunnicliffe missed out on a start against one of his former clubs, dropping to the bench as Corry Evans returned from suspension.
It was a slow start to proceedings in the Suffolk sunshine, but when the game sprang into life it was Rovers with the better opportunities in the first half.
Lee Williamson saw a shot deflect just wide, whilst a flying Rudy Gestede just couldn't keep his header down from Craig Conway's whipped centre.
On 27 minutes Rovers really should have taken the lead. As Jason Steele free-kick was flicked on by Gestede, Tom Cairney picked out Jordan Rhodes but his header lacked power, then as keeper Dean Gerken and Jonathan Parr looked to clear they got in each others way, but as the ball dropped to Shane Duffy he didn't react quick enough and the chance was gone as quickly as it arrived.
Gerken was kept busy once more as the half drew to a close, saving well one-handed at his near post after Rudy Gestede had got the better of Tommy Smith.
Aside from a couple of high balls that were claimed well, Steele had a relatively quiet time at the other end, but he was in the right place at the right time to save well when David McGoldrick chanced his arm with a shot from the edge of the box.
Rovers continued to force the pace as the half drew to a close, but they couldn't grab the goal their first half play merited.
The start of the second half saw the home side come out with a greater enthusiasm, immediately putting Rovers under pressure.
A David McGoldrick through ball set Conor Sammon racing goalwards only to be tripped by Matt Kilgallon on the edge of the box. The home fans bayed for a penalty and a red card, but with Rovers having men back and the challenge outside the area, a free-kick and a yellow was the decision after lengthy deliberation.
David McGoldrick stepped up to take the free-kick but bent his effort a couple of yards wide of Steele's goal.
Rovers appeared to have ridden the storm but on 64 minutes they were reduced to ten men.
As McGoldrick slipped the ball through for Sammon to chase the Town striker appeared to foul Kilgallon, but referee James Adcock blew for an offence from the Rovers man and quickly issued the defender a second yellow followed by a red, bringing a swift end to his return to the team.
McGoldrick stepped up to take the free-kick and on this occasion he made no mistake, curling the ball into the top corner beyond Steele.
Sixty seconds later Rovers had Shane Duffy to thank for keeping it at 1-0, a ball into the area was headed goalwards by Stephen Hunt, but the Irishman cleared off the line.
Alex Baptiste replaced Craig Conway and Adam Henley came on for Rhodes as Rovers looked to shore up the defence, but it was the home side who looked to take advantage of the extra man, McGoldrick the width of a post away from doubling their advantage, whilst defender Tommy Smith headed over a Stephen Hunt corner when well placed.
Despite their dominance, Rovers should have grabbed an equaliser six minutes from time, Evans clipping a ball into the box for Duffy, but the defender put his header wide of goal.
With Rovers pushing up McGoldrick almost added a second two minutes from time. A long ball from Gerken flicked off the head of Williamson to send the striker clean through on goal, but Steele saved well low to his left.
With four additional minutes there was just enough time left for late drama, and as Shane Duffy, deployed as an emergency striker, turned Christophe Berra just out side the area, only to be brought down. Ben Marshall stepped up and curled a wonderful free-kick into the top left corner of Gerken's goal.
After their first half display a point was certainly deserved, but the home side will rue missed chances in the second against the ten men.
IPSWICH TOWN: Gerken, Parr, Mings, Smith, Berra (c), Skuse, McGoldrick, Hunt (sub Ambrose 90+3), Bru (sub Anderson 85 mins), Sammon, Williams (sub Tabb 79 mins).
Subs not used: Bialkowski (GK), Bajner, Henshall, Clarke.
Goals: McGoldrick 65 mins.
ROVERS: Steele, Marshall, Duffy, Kilgallon, Olsson, Cairney (sub Tunnicliffe 83 mins), Evans, Williamson, Conway (sub Baptiste 68 mins), Gestede, Rhodes (c) (sub Henley 75 mins).
Subs not used: Eastwood (GK), Dunn, Varney, Taylor.
Goals: Marshall 90+3 mins.
Booked: Kilgallon, Tunnicliffe, Marshall.
Attendance: 16,972 (including 379 Rovers supporters)