By Clare Fallon

LONDON (Reuters) - Six-times champion Roger Federer came back from the brink of a dramatic first-round exit at Wimbledon Monday, recovering from two sets down to beat gritty Colombian Alejandro Falla 5-7 4-6 6-4 7-6 6-0.

"I definitely got very lucky out there," Federer said in a interview as he came off court.

"I have lost many matches this year which I should have won; this is one I should have lost but I came through. But that is sometimes how grass court tennis works."

The Swiss top seed, who also recovered from 4-4 0-40 on his serve in the third set, finally found his game after being made to look second best for much of the match before a disbelieving Center Court crowd.

He wrapped up the fourth set tiebreak 7-1, spurred on by chants of 'Roger, Roger' from the crowd as the two men changed ends. Then he galloped through the decider in double quick time, avoiding the ignominy of being the first Wimbledon champion to fall at the first hurdle since Lleyton Hewitt in 2003.

Federer, who pummeled Falla for the loss of three games in the tune-up event in Halle last week, looked lost in the middle part of the match as the Colombian returned superbly, picked his advances to the net exquisitely and matched the 16-time grand slam winner stroke for stroke from the back of the court.

THIGH TREATMENT

When Federer won the third, Falla, who had several bouts of treatment on his left thigh from the trainer during changeovers, could have been expected to fold.

However, the Colombian, who had been dismissed as "cannon fodder" in an article in the day's official program, broke in the opening game of the fourth, with Federer contributing to his total of seven double faults in the process.

Falla saved one break point at 5-4 with an ace but could not hold his nerve on the second, hitting a forehand long as the Federer fans erupted.

There was little doubt about the outcome when Federer took the match into a fifth set, which he won in 27 minutes. Once the Swiss had gone two breaks up, Falla won only four more points in the match and one of those came when Federer slipped on the grass and sat down.

The two men left Center Court to a standing ovation, with the crowd reserving a special cheer for the valiant Falla.

Federer will face Serbian qualifier Ilija Bozoljac in round two.

(Editing by Miles Evans)