By Claudia Parsons

NEW YORK (Reuters) - Serbian third seed Novak Djokovic survived a tough challenge from big-serving Croatian teen-ager Marin Cilic 6-7 7-5 6-4 7-6 in a late-night slugfest to reach the fourth round of the U.S. Open on Sunday.

Djokovic, the 21-year-old Australian Open champion who lost last year's Open final to Roger Federer, was matched stroke for stroke by the 19-year-old Cilic, seeded 30th and playing in his first U.S. Open.

"I had a very, very difficult match and even if I lost today, he would deserve it," Djokovic said in a courtside interview after nearly four hours on the Arthur Ashe Stadium court. "He absolutely played great."

They battled fiercely in the first set in long rallies that drew gasps from the crowd, with Cilic showing his youthful speed and extraordinary reach to retrieve what seemed like certain winners.

Both players saved set points in the opening tiebreaker before Cilic used a big serve and powerful groundstrokes to win it 9-7.

In the second, Cilic saved a break point at 5-5 but allowed Djokovic a second which the Serbian pounced on to win a crucial game and serve out the set.

"I was just trying to stay with him, I knew he had a great serve, great first-serve percentage," Djokovic said. "I used my chances, I stayed focused."

Cilic served 19 aces in the match to Djokovic's eight, but the go-for-broke Croatian outpaced him on double faults, with 12 to three.

The third set was equally hard fought but 21-year-old Djokovic was more consistent, forcing Cilic to run from corner to corner, wearing him down.

The world number three served for the match at 5-4 in the fourth set and had two match points from 40-15, but Cilic came through with great returns of first serves followed by sizzling groundstrokes to save them and even up the set.

In the decisive tiebreaker, Djokovic delivered a knockout blow, steam-rolling through to win it 7-0.

Next up for Djokovic will be 15th seed Tommy Robredo of Spain.

(Editing by Larry Fine)