Scotland took the lead after just 10 minutes when Charlie Mulgrew diverted James Morrison's strike beyond goalkeeper Austin Ejide with an improvised back-heel which looped into the back of the net.
Grant Hanley found himself involved at both ends when his header was disallowed for a shove on Ejide, before his deflection took Michael Uchebo's effort past Allan McGregor as Nigeria pulled level before the break.
Gordon Strachan's side then found retook the lead when Azubuike Egwuekwe put Alan Hutton's cross through his own net under the close watch of James Morrison, but Nwofor fired in a late equaliser following some lacklustre defending.
Reports in the build-up were dominated by allegations that the National Crime Agency, which investigates serious and organised crime, asked FIFA to issue an alert over attempts to fix the game at Craven Cottage.
The match went ahead despite those claims, which are understood to be under police investigation, and few could have foreseen the goals that punctuated the Tartan Army's 2-2 draw with the African champions.
There was a fantastic atmosphere at Craven Cottage, with the noise going up a further few decibels after just four minutes as Ikechi Anya broke behind the Nigeria defence.
Latching onto a fine ball forwards from Morrison, the Watford flyer saw his goal-bound strike graze the far post after a slight deflection off Kunle Odunlami.
Scotland would not have to wait long to beat goalkeeper Austine Ejide, though, thanks to a mixture of quick thinking and luck on Mulgrew's behalf, meeting a 20-yard Morrison strike with a flick which looped into the top-right corner.
The Tartan Army were standing firm and, after the returning Shaun Maloney saw a hopeful 30-yard strike fly over, looked to have doubled their advantage when Hanley leapt to meet a corner, only for referee Lee Probert to chalk the goal off for a foul on Ejide.
The Nigeria goalkeeper was fortunate to see that goal scrapped after his feeble attempt to gather and was almost caught out again when Maloney whipped in a cross from the right shortly afterwards.
Scotland were still in the ascendancy at this point but were caught cold as the Africans got a lucky goal of their own, with Uchebo bursting through the middle and hitting a 25-yard strike that deflected in off Hanley.
Shola Ameobi hooked a volley goalwards and struck wide before the break, with the recently released Newcastle man continuing to struggle in front of goal when play resumed.
A wicked deflection saw the ball fall into his path just four minutes after the restart, only for the big striker to be denied from close range by McGregor's feet.
With Nigeria having failed to clear their lines, Alan Hutton sent in a low cross from the right and Egwuekwe directed past his own goalkeeper under pressure from Morrison.
Having seen Scotland bring on Derby's Chris Martin for his debut at half-time, Keshi introduced Nosa Igiebor and Stoke's Peter Odemwingie, who had not represented his country since February 2012.
The substitutes linked up immediately and the latter's low strike smothered by McGregor, before Scotland celebrated a third - only for the offside flag to see Maloney's close-range effort from Hutton's low cross cancelled out.
Martin stung the palms of Ejide in a bid to add to the 25 goals he scored for Derby this campaign as Nigeria struggled to make a telling impact.
Victor Moses hit a fizzing 20-yard strike over and Nwofor missed two headers of differing difficulty, before finally finding the net.
Gordon Greer hit the deck in a challenge with Nwofor, who reacted quickly when the ball came back into the box to fire past McGregor from an acute angle.