|ATP World Tour Finals, O2 Arena London, 9-16 November|
|Coverage: Afternoon sessions (14:00 GMT) and first semi-final (14:00 GMT) on BBC2/BBC website, final on BBC3/BBC website (19:00 GMT); live commentary of each match on 5 live sports extra, live text commentary on BBC website|
Britain's Andy Murray kept his ATP World Tour Finals hopes alive with a straight-sets win over Milos Raonic at the O2 Arena.
Murray would have been been eliminated with a defeat but came through a tense match 6-3 7-5.
He will face Roger Federer in his final Group B encounter on Thursday, with a semi-final place still up for grabs.
Federer earlier beat Kei Nishikori 6-3 6-2 to top the standings after two matches.
"On Sunday, there wasn't much magic," said Murray. "Today I came up with some good shots in the right moments. Milos didn't serve as well as he can and that helped."
The signs had not been particularly good for Murray heading into Tuesday's do-or-die contest after a poor opening display against Nishikori and with only one win in four matches against Raonic.
There was plenty on the line for the Canadian too, however, and it was Murray who coped better with the occasion.
That he was able to clinch victory in two sets could prove decisive when the final standings are calculated.
"I obviously played better tonight," said the Scot. "I hit the ball a lot cleaner than I did on Sunday from the beginning of the match, so that was pleasing.
"I was going in knowing that if I lost the match, I was out. It kind of didn't really feel like a round-robin anymore. It was more like a knock-out."
Raonic appeared nervous throughout and his major strengths completely deserted him as he made 23 errors on the forehand side and just 38% of first serves in the opening set.
Murray was frustrated to miss out on two break points when presented with second serves in game four, but Raonic helped him out two games later with a double fault, a wayward smash and another missed forehand.
There was a slight wobble when he failed to convert two set points in game nine, but a good serve wrapped it up and another Raonic error gave the Briton an early break in the second.
|BBC tennis correspondent Russell Fuller|
|"Further progress in the tournament is far from guaranteed, but of most importance right now is that Murray played significantly better than he had against Kei Nishikori on Sunday afternoon. Raonic contributed generously to his own downfall with a catalogue of errors, but Murray was sharper and more animated - and is therefore still in with a chance of reaping the dividends of his 15,000-mile round trip to qualify."|
It was never likely to be straightforward, however, and Raonic found a moment of magic with a forehand half-volley to earn a break-back point that Murray handed over with a loose backhand for 2-2.
Finally, the huge Raonic serve clicked into gear and he was able to put pressure on Murray, but the Scot came through two testing service games and made the decisive move at 5-5.
A superb running pass set the tone and with another break point on offer, Murray fired over a dipping backhand that caught out Raonic at the net.
The tension was clear to all when Murray's first match point whistled by as a tame 77mph second serve was hammered past him, but Raonic's 33rd error of the evening - confirmed by Hawkeye - brought an end to the contest.
A thrilled Murray leapt in celebration, punching the air, and he moves on to face Federer on Thursday evening with a chance to extend his season into the weekend.
"It will be obviously a very difficult match, but it will be an exciting match," added Murray.
"A good one to be part of. I hope I can play well. We've had some very good matches over the years. I hope on Thursday it will be the same."