Visiting Spurs twice led the encounter at St James' Park, but were forced to settle for a share of the spoils following Ameobi's late intervention.
After a slow start to the match, the deadlock was eventually broken in the 40th minute courtesy of a penalty from Rafael van der Vaart. Newcastle defender Steven Taylor was the culprit, tripping up Emmanuel Adebayor inside the area and Van der Vaart dispatched the spot-kick past Tim Krul.
Despite the disappointment of falling behind so close to the break, Alan Pardew's Newcastle hauled themselves level just two minutes after the restart. Jonas Gutierrez was the architect, beating Luka Modric and Kyle Walker before crossing for Demba Ba who scored from close range despite the best efforts of Brad Friedel in goal.
Adebayor then dragged a shot wide for Spurs, but Harry Redknapp would not have to wait too long for his side to edge back in front. Jermain Defoe had only been on the pitch a matter of minutes when he collected possession from Scott Parker and shot low past Krul from the edge of the area in the 67th minute.
Ryan Taylor then warmed Friedel's palms with a free-kick from 25 yards out, before Ameobi struck eight minutes from time.
The 30-year-old striker beat the Spurs offside trap to drive a shot low across Friedel and into the bottom right hand corner of the net.
Newcastle remain in fourth place in the Premier League table, while Spurs are sixth.