Charlie Mulgrew skilfully diverted James Morrison’s strike into the net to give Scotland the lead before Michael Uchebo levelled with a deflected shot.
An own goal by Azubuike Egwuekwe turned the match back in the Scots’ favour early in the second half.
World Cup-bound Nigeria pressed for a second equaliser and were rewarded when Nwofor fired home on the turn.
Gordon Strachan’s men were bidding to become the first Scotland side since 1951 to win four successive away matches.
And they started brightly at the neutral venue with Ikechi Anya firing a low drive on to the post via the heel of Kunle Odunlami.
Scotland’s new-look back four, which included Dundee United’s Andrew Robertson making his first international start, found themselves under pressure when they conceded possession to Uchebo but Allan McGregor saved the shot.
Having narrowly escaped on that occasion, Strachan’s men sought to capitalise on a set piece and duly delivered.
Shaun Maloney and Anya teed up Morrison for a low shot that was looped over goalkeeper Austin Ejide by the outside of Mulgrew’s left boot.
The ball was in the Nigeria net again when Grant Hanley rose to meet another Maloney corner but English referee Lee Probert awarded a foul against the Scotland defender for his challenge on Ejide.
Nigeria gradually worked their way back into the match and Shola Ameobi, recently released by Newcastle, volleyed Ejike Uzoenyi’s into the hands of McGregor.
But the Scottish keeper could do nothing when Uchebo’s shot spun into the net off Hanley.
In the first of many substitutions, Derby’s Chris Martin made his Scotland debut at the start of the second half as a replacement for Steven Naismith.
McGregor got down well to block an Ameobi shot and Scotland once again found themselves ahead after an important save from the Hull stopper.
Hutton’s driven cross was knocked back towards goal by Egwuekwe and Odunlami could not prevent the ball from crossing the line.
At the other end, substitutes Nosa Igiebor and Peter Odemwingie played a one-two before the former drew a save from McGregor.
Maloney then converted Hutton’s low cross but was correctly flagged offside.
Chances continued to come Scotland’s way and George Boyd, on for Morrison, set up Martin for a strike that Ejide blocked.
Martin’s club-mate Craig Forsyth joined the fray for his Scotland debut when the impressive Robertson came off, while the introduction of Celtic’s Efe Ambrose for Odunlami was Nigeria’s sixth change.
Nwofor, who had replaced Ameobi, twice threatened with headers before he capitalised on some slack defending to net the final goal.
Hanley’s attempted clearance ricocheted off Nnamdi Oduamadi into Nwofor’s path and the Heerenveen forward drilled past McGregor from close range.
Source: BBC