For one brief moment here yesterday, it seemed like it had all been a dream.

"Runner-up, Maria Sharapova," came the announcement in French and Italy's Sara Errani raised her hands in celebration.

Luckily, Sharapova thought it was all hilarious and the mistake was quickly corrected. The Russian's 6-3, 6-2 victory over the 21st seed gave her a first French Open title and made her only the 10th woman in history to complete a full set of Grand Slam titles.

"It's surreal," Sharapova said, little more than an hour after accepting the trophy from former champion Monica Seles. "It's the most unique moment I've experienced in my career. I never thought I would have that.

"I thought that when I won Wimbledon at 17, that would be the most treasured moment of my career. But when I fell down on my knees today I realised that this was extremely special, and even more so."

Four years after clinching the last of her three Grand Slam titles, Sharapova was back on the winners' podium, perhaps an even sweeter feeling having lost in the final at Wimbledon last summer and again this January at the Australian Open.

When she was forced off the Tour for eight months after shoulder surgery in 2008, there were times when she wondered if she would ever get back to her former level.

Four years later, after an enormous amount of hard work and more than a little soul-searching, the Russian is back as the world No 1 and back where she belongs, as a Grand Slam champion.

For some, that might be enough, but as she further contemplated the scale of her achievements, Sharapova said there was still plenty of winning left in her.

"It's not over yet, you know," she said. "I'm not sitting here and saying I'm done because I'm far from it. I have a lot more in me to achieve. I believe in my game.

"I think that's one of the reasons I'm sitting here with my fourth one and winning Roland Garros, because I always believed I could be better, I could be a better player, whether it was on clay, whether it was on grass, whether it was on cement, anything, I always strive to be better.

"One percent here, a few here, this is what I've always wanted to achieve. No matter how tough it was, no matter how many people didn't believe in me, didn't think that I could get to this point, I didn't care and I didn't listen.

"I always listened to my own voice, and it always told me that for some reason I'm meant to be better. I'm meant to succeed again. And I did."

Having lost at Wimbledon and in Melbourne – both times when she went into the match as favourite – there was a chance she might buckle against a woman who was appearing in her first Grand Slam final.

Errani, trying to emulate the achievements of fellow Italian Francesca Schiavone, who won the title here in 2010 and reached the final last year, had progressed thanks to her brain rather than brawn.

Victories over three former grand slam champions, Ana Ivanovic, Svetlana Kuznetsova and in the semi-finals, Sam Stosur, showed that what she lacked in power, at 5ft 4½in tall, she more than made up for in speed, variety and the sheer cleverness of her tactics.

But it was always going to be tough for her against Sharapova, probably the most aggressive returner on the Tour and a woman who had reached the final for the loss of just one set. Errani's serve, her biggest weakness, was just not accurate enough to get Sharapova off balance and the Russian took full advantage right from the start as she raced to a 4-0 lead.

With the wind making life difficult for both players, Sharapova's serve held up superbly – she hit six aces in total and only five double-faults – but Errani got on the board when she broke the Russian to trail 4-1.

A hold of serve further reduced the deficit but the second-seeded Russian held firm for the rest of the set and then broke in the first game of the second on her way to a 2-0 lead.

Saving a break point at 2-1, she then broke again to lead 4-1 and though Errani broke back – much to the crowd's delight – Sharapova restored her advantage with another break to lead 5-2.

Serving for the match, she was thwarted twice on match point, once with a deft drop shot from Errani, but made no mistake at the third time of asking as she forced the Italian to net a backhand.

As the ball fell short, Sharapova fell to her knees in joy, before celebrating on court by jumping up and down.

For Errani, there is the consolation of rising into the top 10 for the first time.

"I played a good two weeks," Errani said. "It was incredible for me. But I just want to keep doing the same thing that I was doing. I have to just think that it's not a normal thing for me to make the final of a Grand Slam."