Steven Gerrard's side triumphed against Standard Liege and Lech Poznan in their opening two games, but they got off to a poor start at the Estadio da Luz as Connor Goldson diverted a low cross into his own net after just 60 seconds.
They powered back before half-time, though, taking ruthless advantage of Nicolas Otamendi's straight red card for a professional foul through an own goal from Diogo Goncalves and a fine strike from Glen Kamara.
Alfredo Morelos added a third shortly after the restart, but Benfica fought back for an unlikely draw as Rafa's 77th-minute effort preceded Nunez dramatically levelling proceedings with the clock winding down.
Benfica got off to a flier when Goldson turned into his own net from four yards after determined play down the right-hand side from Rafa.
Pizzi dragged wide after 10 minutes from a flowing counter-attacking move before Rangers were handed a lifeline when Otamendi was dismissed in the 19th minute for hauling down Ryan Kent after a long ball over the top.
The Scottish Premiership side took swift advantage of their numerical superiority, pulling level five minutes later when Goncalves comically put through his own net from James Tavernier's cross.
Kamara then put the visitors ahead just a minute later with a drilled effort from 20 yards, while Morelos slotted home a third in the 51st minute from Tavernier's low ball into the six-yard box.
Kent should have made it four, but struck the post with only Odisseas Vlachodimos to beat, with Rangers duly punished for his profligacy.
Rafa pulled one back for the hosts before Nunez slotted past Allan McGregor to seal a draw after being played clean through by Gian-Luca Waldschmidt.
What does it mean? Bitter pill for Gerrard to swallow
Gerrard will be furious with his side for conspiring to draw a game they dominated for long periods. They carved out 13 shots and enjoyed almost 59 per cent possession, while the hosts scored with their only two shots on target after Goldson's early own goal.
The result leaves both sides on seven points at the Group D summit, four points ahead of third-placed Lech Poznan.
Kamara shines for Rangers
The Finland international deserved to be on the winning side, putting the visitors 2-1 up with a well-struck effort and gaining possession nine times – more than any other Rangers player.
Benfica grab a point despite Otamendi's best efforts
Otamendi had his fair share of mishaps while at Manchester City and he was up to his old tricks on Thursday. He was badly caught out by Kent early on and deserved his red card for a clumsy challenge.
Rangers host Hamilton Academical in the Scottish Premiership on Sunday before the international break, while Benfica are in domestic action on the same day against Braga.