Cole turned poacher to cancel out Zat Knight's 57th-minute opener and maintain Pompey's European push.
Fulham looked to be heading for a shock win when Knight rose above the Pompey defence to nod Claus Jensen's corner goalwards. The ball deflected off Pompey captain Dejan Stefanovic and beyond David James' despairing dive and into the net.
The goal handed James the unwanted accolade of becoming the first goalkeeper to concede 500 Premiership goals.
At the other end, Antti Niemi was having an inspired afternoon and pulled off several top-classes saves to keep Pompey out.
Niemi set the tone for the afternoon with a world class one-handed stop to turn Lomana LuaLua's 25-yard free-kick over the bar in the 18th minute.
Nwankwo Kanu had already wasted a golden chance to add to his seven goals for the season when blazed wide from six yards after LuaLua had crossed from the byline.
Sean Davis also came close to netting against his old club when he flicked a glancing header against a post from Stefanovic's cross.
Moritz Volz forced a rare save from James in the 24th minute when he raced on to Jensen's centre and unleashed with a downward header the Pompey keeper did well to scramble off the line.
Niemi was in the thick of the action again in the dying seconds of the half to stop Kanu adding to his amazing early season tally.
Matthew Taylor picked up the gangly Nigerian with a pin-point right-wing corner only for Niemi to punch away his close-ranger header with his outstretched right arm.
Gary O'Neil should have made Pompey's pressure tell six minutes after the restart when he darted into the box to try and get on the end of Taylor's in-swinging centre, but narrowly failed to connect with his flying right boot six yards out.
Knight stunned the home fans by putting Fulham ahead soon after, prompting Redknapp to throw on goal king Cole in search of a leveller.
Linvoy Primus almost became the unlikely hero when his right-foot shot from point-blank range from a Pedro Mendes corner was hacked off the line by Carlos Bocanegra in the 63rd minute.
Another defender, Noe Pamarot also came within inches of equalising with his first goal for the south coast side when he headed against a post from O'Neil's free-kick, four minutes later.
You felt something had to give as Harry Redknapp's men continued to pile forward and poacher Cole notched the 280th goal of his medal-strewn career to draw them level.
O'Neil's corner was flicked on by Sol Campbell and Kanu nipped in ahead of Niemi to push the ball into the path of the grounded Cole, who turned it home from a yard out.
Davis could have stolen all three points late on when he found himself with a shooting chance on the edge of the box, but volleyed well wide of Niemi's goal.