Assombalonga opened the scoring against Ipswich Town before half-time from a controversial penalty to lift Mark Warburton’s men out of the relegation zone after two early goals for Blackburn Rovers at Brentford had dumped Forest into the bottom three.
The striker’s 43rd-minute spot-kick relieved some of the tension on the banks of the Trent but Forest fans knew a big win for Rovers at Griffin Park could still send them down to League One on goal difference with the sides beginning the day level on points.
Those fears were allayed when club captain Chris Cohen rifled home their second goal on 57 minutes and Assombalonga blasted in his second on 69 just three minutes after having a second penalty saved.
It meant the former European Cup winners’ anticipated takeover by controversial Evangelos Marinakis will go ahead with the club still in the second tier despite a major scare.
Forest put Ipswich under immediate pressure as they set out their intentions in a frantic opening 90 seconds.
A fine turn and cross by Eric Lichaj sparked an attack that led to a corner for the home side.
And from the flag kick came a scramble on the edge of the area that saw Forest defender Matt Mills strike a shot that was charged down by Christophe Berra
And the move was kept alive with Jamie Ward curling a shot just wide of Bartosz Bialkowski’s far post.
But there was a serious scare for Forest moments later when Ipswich, who had offered little in the early stages, went close through Grant Ward.
His long-range effort was heading for the top corner until home goalkeeper Jordan Smith took off to his right to palm it away.
News of early goals for Blackburn and Birmingham, who were also under threat of relegation, sucked the life out of a previous boisterous home crowd.
But the home side ought to have taken the lead 11 minutes before half-time as their wing-backs combined to good effect.
Ben Osborn tore down the left and crossed for Lichaj, who arrived from the right, but sent a shot over from eight yards out.
But the hosts were living on the edge and they survived a huge scare seven minutes before the interval when Smith reacted superbly to push a deflected drive by Dominic Samuel onto the crossbar.
Two minutes before the break, Warburton’s men got their breakthrough as referee Andy Davies made a crucial decision.
He punished Bialkowski controversially for a block on Jamie Ward as the forward’s chip over the goalkeeper was being headed off the line.
Assombalonga kept his composure and rifled the penalty into the roof of the net.
Assombalonga should have eased Forest nerves with a second goal on 50 minutes when he held off Luke Chambers to control a high ball, but he could was eased out superbly by full-back Jordan Spence.
But Cohen then lifted the roof off the City ground with the goal that gave his side a hint of breathing space.
It was a patient build-up followed by a powerful strike as Cohen collected a pass from David Vaughan and hit a shot to deflected past Bialkowski and into the roof of the net.
On 66 minutes Forest should have made sure of survival when Jamie Ward raced onto Assombalonga’s pass and was bundled over by substitute Josh Emmanuel.
But this time Bialkowski made a fine save, leaping high to his left to deny Assombalonga another goal from the spot.
It took just four more minutes for Assombalonga to make amends, however, as he wriggled free from two defenders and lashed a shot past Bialkowski at his near post and into the top corner.
Forest were forced to play out five minutes of added time with 10 men as, with three substitutes already used, Osborn suffered a shoulder injury, but by then there was little doubt that their safety was secure.
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