Serena Williams saved her unbridled joy, her leaping ecstasy, for after the handshake, seemingly unsure in the moment of victory whether she had served an ace, whether an enormous struggle was over, whether she really had won her sixth Australian Open, and 19th grand slam singles title. Then came the celebration. It was worth the wait.

Williams has been unwell for much of the past week, plagued by coughing fits, her Friday practice schedule interrupted by a little spell in bed before she was able to complete her preparation for a 23rd grand slam final. She is now 19-4, an extraordinary record. This one was in straight sets, but perhaps misleadingly, for Sharapova made her earn it in a highly-competitive, animated and emotion-charged second, in particular.

Williams was already the oldest Australian Open women's finalist, surpassing Chris Evert, and has now succeeded last year's winner, mother-to-be Li Na, as the oldest champion. In the Open era. only Martina Navratilova at 33 years and 263 days at 1990 Wimbledon has been a more senior major winner than Williams, who is 136 days younger.

Navratilova presented the trophy on Saturday night, but has now been left behind on 18 majors, equal with Chris Evert, while Williams rises to equal third on the all-time list with 20s and 30s star Helen Wills Moody, behind only Steffi Graf (22) and Australian Margaret Court (24).

It was 6-3, 7-6 (7-5). It took one hour, 51 minutes. It was one to remember.

Williams recalled how as a child she she "wasn't the richest, but I had a rich family in spirit and support. Standing here with 19 championships is something I never thought would happen. I went on court with a ball, a racquet and hope, that's all I had. And it's an inspiration for you guys who want to be the best - you can be, never give up and you don't know who you can inspire. I'm so honoured to be here standing with my 19th title – I'm just so excited."

She paid a tribute to her coach Patrick Mouratoglou in what she quipped was the longest speech of her career, after her 17th win in 19 matches against Sharapova.

The pair may not be friends, but they share the fighting qualities of champions, and each was graciously respectful of the other at the presentation. Sharapova congratulated her opponent on "creating history", and said she was enormously honoured to play against her. "I haven't beaten her in a really long time, but I love every time that I step on court against her because she's been the best, and as a tennis player, you want to play against the best."

Still is. Williams broke serve in the opening game on a match in which the first 24 minutes — to 3-2 and 30-30 on the Williams serve — were played with the roof partly open, and the last 87 with the lid fully closed to the rain, thus becoming the fourth women's final to have an indoor element, at least.

Williams has now won three of them and, indeed, the American in this mood and serving at this level, would probably beat anyone, anywhere. Sharapova has been a favourite whipping girl since the Russian's most recent win, back in 2005, and this loss to the other half of the world's highest-profile, highest-earning, most successful duo her 16th in a row.

The rain came at an unhelpful time for Sharapova, who had started to settle into the match, the previous point drawing an animated "C'mon" from Williams after a strong first serve had enabled her to level at 30-all. As the roof closure was completed, Williams retreated inside the tunnel, while Sharapova spent the 12 minutes on court.

Williams came and coughed, and went again, threw up - "I was able to clear it out", she said later -, but eventually returned to win six consecutive points, and thus the double-break. But she dropped her own serve, surprisingly, at 5-3, only to savage Sharapova's again, one cross-court forehand at full stretch a particular gem. The first set lasted about 35 minutes in playing time, as the course of the match seemed set.

But it tightened up again after Sharapova was forced to save two break points early in the second set, an off-forehand winner drawing a loud self-exhortation from the second seed. The Williams answer: three aces before the game was over, and a couple of furious c'mons of her own. Two fabulous competitors; so much feeling. Fondness, not so much.

There was an interesting moment in the seventh game, when Williams served what she thought was an ace on game point, and did the "c'mon" thing again just as Sharapova managed to get her racquet on the ball. Chair umpire Alison Hughes invoked the hindrance rule that had so enraged Williams during the 2011 US Open fainl against Sam Stosur, but this time the American remained calm, saved a break point, and showed her lighter side with a belated, theatrically-muted mock celebration a few points later.

The one at the end was far more robust, but was still some compelling distance away, Sharapova match point down in the 10th game, and saving it, as she had the two in the second round against Alexandra Panova, with a clutch forehand winner.

The next came in just the third tiebreak the pair has played in 19 matches, Sharapova saving another championship point with another great forehand, a let called on a would-have-been Williams ace on the third, but nothing in the way of the last clean winner, her 18th ace. She seemed unsure for a moment, before the result was confirmed.

After the handshake, cue the celebration, the jumping, the ecstasy. It had been five years since Williams' previous Australian Open victory. Like the reaction, it was also worth the wait.