Stephen Keshi's men headed into the game having clinched their place at next year's FIFA World Cup with a playoff win over Ethiopia on Saturday.
And the African nation carried that momentum into the friendly clash at Craven Cottage, producing a determined performance against the four-time World Cup winners.
Italy were on top for much of the encounter and took the lead early on thanks to Giuseppe Rossi.
Nigeria launched a superb fightback, though, Ameobi setting up Bright Dike for the equaliser before giving his side the advantage with a fine improvised volley.
Cesare Prandelli's side did level through Emanuele Giaccherini, but there were to be no further goals despite numerous opportunities for both teams.
Paris Saint-Germain goalkeeper Salvatore Sirigu replaced Gianluigi Buffon in goal for Italy, while Fiorentina striker Rossi was included up front as Prandelli made eight changes to the side that drew 1-1 with Germany on Friday.
Newcastle United forward Ameobi was among those recalled to Nigeria's line-up.
Nigeria had the better of the opening exchanges, but it was Italy who took the lead 12 minutes in, Rossi converting with a delicate finish following great hold-up play from Mario Balotelli.
Sirigu producing a strong save to prevent Ogenyi Onazi's long-range effort from finding the net as Nigeria sought an immediate reply.
Italy dominated for the majority of the half, though, and had opportunities to double their lead, Milan duo Ricardo Montolivo and Balotelli both spurning clear chances.
Despite Italy's dominance, Nigeria levelled things up 10 minutes before half-time when Dike rose highest to head home Ameobi's superb cross.
There was a further shock for Italy five minutes later as Ameobi cleverly converted Francis Benjamin's near-post delivery to give his side an unlikely lead.
Balotelli came close to a stunning equaliser as half-time approached, controlling a deflected high cross in audacious fashion before testing Augustine Ejide with a vicious volley.
Nigeria's lead lasted only two minutes into the second half, Giaccherini slotting under Ejide after Rossi had linked up with Antonio Candreva.
Substitute Marco Parolo twice had the chance to put Italy in front for a second time, blasting over from point-blank range after substitute goalkeeper Victor Enyeama had pulled off a fine stop from an Andrea Pirlo free-kick, and then seeing a deflected effort strike the post.
Balotelli and Nigeria substitute Emmanuel Emenike each squandered clear openings in the closing stages, but neither side could find a winner.
The closing stages provided particularly frantic fare as play switched from end to end, much to the delight of those in attendance.