The Norwich City loanee was sent on as a half-time substitute and scored a cracking 63rd minute goal after playing a one-two with Sammie Szmodics. Mumba’s run and finish was very Siriki Dembele-like and propelled Posh into the fourth round for just the third time in 18 seasons.
They made hard work of it though. They created enough promising situations to have scored six, but needed goalkeeper Dai Cornell to make three saves in quick succession in the final 10 minutes to thwart visiting substitute Brett Pitman. Posh never looked secure at the back which is a concern given Rovers sit 18th in League Two, 43 places below Posh in the Football League ladder.
Szmodics had given Posh a 20th minute lead at a time of total dominance with Rovers getting a lifeline from a soft penalty decision 10 minutes later.
Posh then bossed the opening 20 minutes of the second-half before Rovers rallied in a very entertaining end-end-end final quarter of the game.
Posh boss Darren Ferguson could find no room in his starting line-up for Mumba which was a surprise and no room in a matchday squad of 20 for Mark Beevers or Kwame Poku, presumably the latter was injured or ill. He did recall Szmodics to play up front with Dembele. Former Rovers striker Jonson Clarke-Harris dropped to the substitutes’ bench in the only change from a Posh team that last saw action 21 days previously.
Rovers had been out of action for 28 days and they looked the rustier of the two sides at the start. They set out with a defensive shape, but played a high defensive line that asked for trouble against two mobile forwards.
Jack Taylor and Szmodics breached that line inside two minutes, but the latter rushed his shot and fired wide.
Jorge Grant then found himself beyond the back line and his cross was defended with referee Davies giving a goal kick. It wasn’t his last bad decision of the half.
A superb 16th minute move with two cross-field passes from Josh Knight and Joe Tomlinson led to Nathan Thompson bearing down on goal, but visiting ‘keeper James Belshaw was off his line quickly to save.
A goal looked inevitable and it arrived on 20 minutes when Oliver Norburn’s through ball was chased by Szmodics who prompted Belshaw to deliver an airkick and then tapped the ball into an empty net.
It was one-way traffic although Rovers had looked a threat when launching the ball forward. A quick free kick on six minutes led to Posh ‘keeper Dai Cornell saving on his line after the ball had rebounded off Ronnie Edwards.
Knight was caught ball watching, but Posh scrambled the ball clear amid penalty claims straight after the opening goal and then on the half hour referee Davies intervened. Cornell probably should have been off his line quicker to collect a hopeful punt forward, but he merely stood his ground as Anthony Evans poked the ball past him. Evans ran into Cornell and after a strange little wait Davies decided it was a penalty.
Former Posh midfielder Paul Coutts, a player signed twice by Ferguson, scored from the spot and the goal had a marked effect on the rest of the half as Rovers grew in confidence and Posh wilted. Passes that had been precise became rushed as Posh frustration grew.
Posh sent on Mumba for his debut at the break with Tomlinson making way and his presence appeared to lift his teammates and the crowd.
Dembele shot wide after a decent Grant pass and then the attacking wizard slalomed his way through the defence before a terrific Trevor Clarke block sent the ball over the crossbar. Not that Davies noticed as he gave a goalkick.
Dembele then played Grant through, but Belshaw was out swiftly to block. The pressure had to tell and Mumba sent Posh back into the lead in style.
Dembele and Szmodics then saw close range shots blocked in the same attack after Davies ignored a blatant foul on Grant inside the area before Dembele underhit a pass to Szmodics after the pair broke clear.
Szmodics had his revenge 10 minutes from time when bursting away. He could have rolled Dembele in for a tap in, but instead shot wide.
Struggling sides always fear the worst when chances are missed and Rovers pushed forward on the final stages against a defence - one largely unprotected by midfielders - creaked.
Cornell reacted well to tip Pitman’s deflected shot behind, smothered another close range effort and then stood up tall to beat away a fierce strike before Zain Westbrooke curled wide from 20 yards after one of many Rovers’ corners.
The Posh game management in those final moments was poor, and they survived the ball being headed into the back of their net from a corner but the whistle appeared to have gone well before the ball hit the net. Posh survived though and hopefully the confidence-boost from winning will outweigh the concerns caused by some of the performance.
Posh: Dai Cornell, Joe Tomlinson (sub Bali Mumba, 46 mins), Ronnie Edwards, Josh Knight, Nathan Thompson, Oliver Norburn, Jack Taylor, Harrison Burrows (sub Clarke-Harris, 87 mins), Jorge Grant, Siriki Dembele (sub Ricky-Jade Jones, 90 + 1 min), Sammie Szmodics.
Unused subs: Will Blackmore, Frankie Kent, Ricky-Jade Jones, Kai Corbett, Joe Ward, Kyle Barker, Luke Harris.
Rovers: James Belshaw, James Connolly, Luke Thomas (sub Max-Edwards-Strryjewski, 90 + 3mins)., Zain Westbrooke, Sam Nicholson, Paul Coutts, Nick Anderton Antony Evans, Sion Spence (sub Brett Pitman, 68 mins), Luca Hoole, Trevor Clarke
Unused subs: Jed Ward, Pablo Martinez, Ryan Jones, Jerry Lawrence, Lucas Vaughan, Malik Sesay, Max Edwards-Styjewski.
Goals: Posh - Szmodics (20 mins), Mumba (63 mins).
Rovers - Coutts (pen, 30 mins).
Posh - Norburn (foul).
Referee: Andy Davies 4
Attendance: 4,937 (483 Rovers).