* American fights back after dropping first set
* Williams continues win streak over Russian
* Sharapova loses Miami final for fifth time (Adds detail, quotes)
By Simon Evans
MIAMI, March 30 (Reuters) - World number one Serena Williams fought back from a set down to beat Maria Sharapova 4-6 6-3 6-0 and win the Sony Open for a record sixth time on Saturday as she continued her dominance over her closest rival.
With the win, Williams, who struggled with her serve in the first two sets, becomes only the fourth woman in the Open era to win the same WTA tournament six times, joining Martina Navratilova, Chris Evert and Steffi Graf.
"I finally have some record," Williams said. "Like it's really cool. I can't seem to catch up with Margaret Court or Steffi or anything. I'm really happy to have something right now, so it's exciting.
"Maria played really the best I have seen her play, and I think she was moving unbelievable and she was hitting winners from everywhere. .... How did I end up winning when I actually wasn't on top of my game?"
Second-ranked Sharapova has now lost to Williams in their last 11 meetings and has not beaten the American since her two victories in 2004.
To add to the pain, the match was Sharapova's fifth Miami final and her fifth defeat.
"I had my chances. There's no reason why I couldn't win the match today," said the Russian, who dismissed any suggestion of a psychological weakness against Williams.
"It was a step in the right direction and there's no doubt that we'll be playing many more times. There's no doubt I'll be able to beat her."
Sharapova, who won at Indian Wells earlier this month, took her great form into the opening set, almost breaking Williams in a marathon third game featuring some outstanding baseline rallies.
The Russian, playing sparkling all-round tennis, got her reward when she broke to go 3-2, with a powerful backhand shot that Williams could only return to the net.
Williams broke back straight away though, but a confident Sharapova took advantage of some over-hitting from the American to break in the ninth game and served out to win the set.
It looked as though Sharapova had a real chance to finally end her nine-year winless streak against the American but, as so often, Williams refound her game in the second.
"I was just making so many errors, and I just was like, 'Serena, are you really going to get to the final and not play up to your potential?'" said Williams.
After some entertaining exchanges, a double-fault from Sharapova handed Williams a break point and the Russian's return to the net gave Williams a 5-3 lead and she held to force the third set.
The match turned decisively in Williams' favour when Sharapova produced two double-faults to go down 3-0 in the third set and the Russian never was able to claw back from that position.
"I was losing a little bit of pace on my ball which hurt me," said Sharapova. "Against a player like Serena, you can't really do that."
Williams, who has 15 Grand Slam singles titles, was happy to claim the record but was far from satisfied with her performance.
"One of the first things I said (after the match) is I need that tape so I can go home and study it and train and try to get better," she said.
Reporting By Simon Evans, editing by Gene Cherry