* Djokovic fends off Fognini in three sets
* Murray fights back after losing opening set
* Fish advances in first event since 2012 U.S. Open (Updates with later matches)
INDIAN WELLS, California, March 10 (Reuters) - Australian Open champion Novak Djokovic and third seed Andy Murray both had to work much harder than expected to book their places in the third round of the BNP Paribas Open on Sunday.
Top seed Djokovic lost his bearings in the second set before beating Italy's Fabio Fognini 6-0 5-7 6-2 while Murray had to dig himself out of an early hole on the way to a 5-7 6-2 6-2 win against Russian Evgeny Donskoy.
"It was definitely a difficult challenge today," Serbian Djokovic said courtside after breaking the feisty Fognini in the fourth and eighth games of the third set to claim victory.
"Fabio played very well towards the end of the second set but it was all my fault," said the world number one, who squandered one match point in the 10th game of that set before being broken in the 11th when he netted a forehand.
"I had a very bad game at 4-2, made a couple of unforced errors, got him back in the match. Next thing you know we're one set all and a couple of tight games. I'm just happy to get through."
Djokovic, who had stormed through the opening set in just 19 minutes, wrapped up his fourth win in four matches against Fognini when the 36th-ranked Italian netted a backhand.
The Serb, a perfect 14-0 this year after winning the Australian Open in January and the Dubai Championships last week, will next meet Bulgarian Grigor Dimitrov, a 6-4 6-4 winner against Australia's Matthew Ebden.
"My confidence level is high obviously because of the run I had this year," Djokovic said. "Game-wise, everything works. I feel good about myself."
U.S. Open champion Murray, showing signs of rust in his first tournament on the ATP circuit for six weeks, lost a wildly fluctuating opening set, where he trailed 1-5 at one point, before seizing control of the match.
In blazing desert sunshine at Indian Wells, the 25-year-old Scotsman broke Donskoy's serve twice in the second set and also in the third before sealing victory after two hours 17 minutes when his opponent sent a backhand service return long.
"I've struggled here the past couple of years, I haven't won a match," said Murray, who had not played competitively since losing to Djokovic in the Australian Open final.
"I was a little bit nervous in the beginning and he started very, very well ... he came up with some unbelievable shots. I just tried to hang in there and was hitting the ball much better by the second set."
World number three Murray, a runner-up at Indian Wells in 2009 and a losing quarter-finalist in 2010, said he had initially struggled against the 83rd-ranked Russian's style of play.
"I never saw him play before, so you don't know the patterns particularly well," he added. "He's pretty smart on the court, too. He doesn't kind of go for shots that aren't on and doesn't make many mistakes.
"And I have not played a match for six weeks, so you can't expect to play your best tennis straightaway. He played some really good stuff in the first set. Once I got into more of a rhythm I was able to dictate more of the points."
The 22-year-old Donskoy was playing against a top-10 opponent for only the second time in his career. He lost to 10th-ranked fellow Russian Mikhail Youzhny in the second round at St. Petersburg in 2010.
In other matches, American Mardy Fish made a triumphant return to the ATP Tour after being sidelined since last year's U.S. Open because of a heart condition, battling past compatriot Bobby Reynolds 6-3 3-6 6-4.
Eighth-seeded Frenchman Jo-Wilfried Tsonga beat American wildcard James Blake 7-6 6-4, Nicolas Almagro swept past fellow Spaniard Daniel Gimeno-Traver 7-5 6-1 and Germany's Tommy Haas beat Spaniard Pablo Andujar 6-3 7-6. (Reporting by Mark Lamport-Stokes; Editing by Larry Fine/Peter Rutherford)