Skipper on the night, Keane opened the scoring with a sublime dipping volley after 57 minutes and it looked like we'd finally found just reward after creating numerous chances when Steed Malbranque followed in Aaron Lennon's shot for 2-0 15 minutes later.
But there was a sting in the tail. Anthony Gardner was harshly penalised for a foul on Diego and although Paul Robinson saved Paulo Jorge's spot kick, the taker slotted home the rebound for 2-1. Then home side were level, Ze Carlos flicking home at the near post with 10 minutes remaining.
However, we still looked capable of scoring again and did just that in added time. Didier Zokora threaded the pass through to Keane who was through one-on-one and slotted past Santos for the win we deserved.
Martin Jol made three changes from the win at West Ham with Didier Zokora, Steed Malbranque and Keane in for Jermaine Jenas, Hossam Ghaly and Jermain Defoe respectively, JD on the bench.
There was quite an atmosphere bubbling inside the Estadio Municipal de Braga with the home support in fine voice for the late kick-off. The travelling Spurs army were out in force with flags very prominent around this distinctive arena.
It was very nearly away celebrations first when Dimitar Berbatov strode forward to the left of the penalty area and eased past his marker before poking the ball just the wrong side of the post.
Braga, decked out in the colours of you know who, obviously like a big squad number, with only two players wearing a single digit on the back of their shirts - the rest including an 87 and a 77.
In the 12th minute Keane and Berbatov combined to provide a shooting chance for Tainio and the midfielder stung the palms of Paulo Santos in the home goal. Paul Robinson then had to be alert at the other end to divert a deflected shot from Pinto.
In the 21st minute Steed Malbranque dissected the Braga defences with a deceptive throughball to Berbatov but, with the Bulgarian looking sure to open the scoring, he pulled his shot just wide of the right hand upright.
A cross from Filipe caused a little concern when Gama connected at the far post, but Robinson was on hand. Then a Berbatov surge resulted in a shooting chance for Keane and the skipper drilled in a shot that Santos just managed to knock over the bar with the top of his arm.
From a Lee Young-Pyo cross, Keane missed, but Berbatov didn't and Santos was again busy - and again almost straight afterwards from another Berbatov effort. Half-time arrived carrying the feeling that we should have banked an away goal or two from the first quarter of this tie.
Shortly after the break there was a scare when Ze Carlos spun in the area and dispatched a powerful drive just past Robinson's right-hand upright.
The deadlock was broken in some style on 57 minutes when an Aaron Lennon dash led to the ball being squeezed through into the feet of Keane, who proceeded to arrow it into the top right hand corner past the despairing dive of Santos.
Keane could have added to his tally moments later when he planted his head on a Malbranque chip through but, with Braga motionless awaiting an offside decision, his header flashed just wide.
The advantage was doubled on 71 minutes when a typical darting, jinking run from Lennon led to a low drive from the England man that was not fielded by Santos and the ball spilt in front of Malbranque, who smacked the ball into the roof of the net from close range.
Three minutes later the advantage was halved when Anthony Gardner was adjudged to have felled substitute Diego in the area. It looked a tough call and Robinson did well to block Jorge's spot-kick, but the full back was quick to pounce on the rebound and the Braga crowd came to life again.
Just under ten minutes from time the home side were level when a free-kick from the right was nodded home by Ze Carlos - providing a highly unlikely finish to this contest that looked like going only one way.
We still looked like creating chances on the breaks and after a couple of good positions went by the wayside, Keane struck again in injury time, finishing one-on-one from Zokora's pass.
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Robbie Keane made it six goals in his last four games with a dramatic late winner in Thursday night's UEFA Cup Round of 16 first leg against SC Braga.