* Stosur overcomes rain delays to beat tough American
* Kuznetsova, Schiavone, Jankovic lose in Sydney (Updates with later matches, quotes)
Jan 6 (Reuters) - Australia's Samantha Stosur failed to allay fears she could be heading for another early exit at her home grand slam with a scrappy performance in Hobart while a trio of big names tumbled out of the Sydney International on Monday.
Double grand slam champion Svetlana Kuznetsova and French Open winner Francesca Schiavone crashed out of the first round in Sydney, while former world number one Jelena Jankovic also booked an early flight to Melbourne for next week's Australian Open.
Stosur appeared on course become the third grand slam winner to lose on Monday when she struggled at the Hobart International before the top seed overcame two lengthy rain delays, chilly conditions and stubborn American Madison Brengle.
The 23-year-old Brengle won the first set in a tiebreak before Stosur managed to run away with the second and then claimed the third set tiebreak on her fifth match point to clinch the 6-7 (4-7) 6-1 7-6 (7-5) victory.
Stosur, the 2011 U.S. Open champion, has struggled on home soil in the past five years, having not advanced beyond the fourth round, with six first round exits in 14 tournaments in Sydney, Brisbane and the Australian Open.
She lost all three of her matches in the Hopman Cup in Perth before entering Hobart, which had attracted a strong field before a wrist injury forced Italy's Flavia Pennetta to join Venus Williams on the sidelines.
Russia's Kuznetsova, who had a good second half of 2013 to enter the Sydney tournament inside the top 20 after battling back from knee injuries in 2012, was surprisingly beaten 6-3 3-6 7-5 by American lucky loser Varvara Lepchenko.
Schiavone, the 2010 French Open champion, lost 6-4 6-4 to Lucie Safarova of the Czech Republic. The 33-year-old Italian was also knocked out of the first round of the Brisbane tournament last week by Jankovic.
Serbia's Jankovic, the fourth seed in Sydney, was unable to repeat her semi-final run in Brisbane and was swept aside 6-4 6-2 by Russian left hander Ekaterina Makarova, who used her big ground strokes to move the world number eight around the court.
"I tried to be aggressive and not let her attack, because she's really good playing down the line from the backhand," Makarova told the tournament website.
"So I tried to move her to the backhand, not to stand and hit it.
"I was just thinking that it would be a really long match, every point is really long because she never miss those easy balls.
"But I showed my best tennis, and it works really well. I'm happy that I came through."
Denmark's Caroline Wozniacki, playing for the first time since announcing her engagement to golfer Rory McIlroy over the New Year, overcame a tough challenge from Germany's Julia Goerges before she clinched a 3-6 6-2 6-4 victory to set up a second round showdown against Safarova.
American Jack Sock vindicated Auckland Open organisers' decision to give him a wild card with a 6-3 6-4 victory over France's Adrian Mannarino to set up a second round clash against second seed Tommy Haas of Germany. (Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)