A second half header from Sam Gallagher rescued a point for Rovers in a tough encounter at Ewood Park.
The visitors dominated for long spells following Tammy Abraham's 14th minute opener, but they couldn't grab a second goal their play deserved.
Instead it was Rovers who drew level with 20 minutes to go when Gallagher rose high at the back post to head home a cross from Elliott Bennett.
That prompted a strong end to the match from the home side as they looked to turn the match on it's head. Gallagher saw huge penalty claims waved away after he looked to have been brought down in the area, whilst Jason Lowe and Tommie Hoban were both narrowly off target.
The draw means a four-point haul over the Easter period, and whilst Rovers remain in the bottom three, they've gained ground on the teams above them in the table.
It was a tentative start at Ewood Park, as the two teams, both unchanged from victories on Friday, looked to ease into the match, but it was the visitors who grabbed the opening goal just 14 minutes into the match.
There seemed little on for either side as the Robins passed the ball about in the centre circle but a lofted pass over the top from Paterson saw Abraham steal into the area and with a deft flick of the right boot he put the ball past the advancing David Raya and into the back of the net.
Rovers looked to hit back straight away and a fine cross from Elliott Bennett picked out Sam Gallagher in the area, but his header was straight into the arms of Frank Fielding.
Josh Brownhill fired a free-kick straight at Raya, whilst a Bennett set-piece at the other end almost saw Derrick Williams pounce against his former club, but Fielding was alert to the danger to claim.
Whilst both sides enjoyed spells with the ball it was the visitors who continued to pose the greater threat up to the break. Following good work from Abraham, Korey Smith hit a low shot from 25-yards that Raya saved low, before the goalscorer over as Rovers failed to clear their lines.
Rovers' poor first half display prompted a double change at the start of the second as Craig Conway and Lucas Joao replaced Ryan Nyambe and Liam Feeney.
It also brought about a change in formation as Rovers' switched to a 4-4-2 with Bennett moving to right back.
Yet it was the visitors who were lively from the restart, Marlon Pack with a long-range strike that whistled just past Raya's right post, before excellent play by Brownhill saw him tee up Matty Taylor who fired over from ten yards out.
Defender Mark Little then skipped his way round the back of the Rovers defence and into the area but his shot was blocked allowing Raya to claim. Before a ball out of defence saw Paterson drive upfield to the edge of the area, his pass was worked into the path of Abraham but the Rovers keeper smartly pushed his effort aside.
With Rovers offering very little in advanced areas, Tony Mowbray made his third and final change as Marvin Emnes replaced Elliott Ward.
But it was Bristol City who continued to look the likelier to get on the scoresheet once more as Abraham tricked his way into the area to tee up Brownhill, but the midfielder's effort lacked purchase and was straight at Raya.
Those missed chances would prove costly for the visitors as Rovers grabbed an unlikely equaliser with 20 minutes to go.
Bennett hit a searching ball from right to left and Gallagher pulled away at the back post to head back across goal and into the far corner of the net for his 12th goal of the season.
Suddenly it was Rovers with the momentum, taking the game to the opposition. Jason Lowe hit a cross-field pass out to Connor Mahoney and as the winger's centre came back out to the captain he planted his shot just the wrong side of the upright.
Seconds later Rovers saw a huge shout for a penalty waved away by referee Mike Jones when Joao threaded the ball through to Gallagher.
Smith twice fouled the striker as he advanced into the penalty area, but the the officials were unmoved.
Rovers continued to press forward in the closing stages with Friday's match-winner Tommie Hoban glancing a Conway corner wide, but despite seeing plenty of dangerous crosses into the box, it just wouldn't drop for a man in blue and white leaving the home side to settle for just a point.
Results elsewhere means Rovers have closed the gap on those teams above them, they continue the fight next Saturday against Wolves at Molineux.
ROVERS: Raya, Nyambe (sub Conway 46 mins), Ward (sub Emnes 67 mins), Hoban, Bennett, Lowe (c), Akpan, Williams, Mahoney, Feeney (sub Joao 46 mins), Gallagher.
Subs not used: Fisher (GK), Guthrie, Tomlinson, Brown.
Goals: Gallagher 71 mins.
Booked: Bennett 22 mins, Williams 54 mins.
BRISTOL CITY: Fielding, Little (sub Cotterill 77 mins), Bryan, Flint, Smith, Brownhill, Abraham, Taylor (sub Wilbraham 86 mins), Paterson (sub O'Dowda 74 mins), Pack, Wright
Subs not used: Giefer (GK), Tomlin, Magnusson, Hegeler.
Goals: Abraham 14 mins.
Booked: Wright 49 mins, Bryan 82 mins.
Attendance: 13,935 (including 1311 visiting supporters).