The American world number one served superbly to win a pulsating final 6-3 7-6 (7-5) after Sharapova fought back in the second set.
Williams, 33, moves past Martina Navratilova and Chris Evert with a 19th major singles title.
She has now beaten Russia's Sharapova, the world number two, 16 times in a row dating back to 2004.
I have to congratulate Maria, she played a wonderful match and she really pushed me," said Williams.
"She played so well and gave me a great final not only for the fans, but for women's tennis. I'm really honoured to play her in the final."
Despite feeling so unwell during a rain delay in the first set that she left the court to vomit, Williams hit 18 aces and 38 winners as she won in one hour and 51 minutes.
Seemingly unsure for a moment that an ace had sealed victory, she then shook hands with Sharapova and bounded over to the corner of Rod Laver Arena towards her player box.
It was a brilliant performance in a final that exceeded many expectations, bearing in mind the players' head-to-head record.
Sharapova made a nervous start, double-faulting to drop serve in game one, while Williams appeared keener than ever to shorten the points, possibly because of her ailment.
The American crushed the Russian's second serve and was not disrupted by a 12-minute rain break that led to the roof being closed.
Still feeling the effects of a heavy cold that has dogged her over the last week, Williams headed off court - in contrast to Sharapova - but the top seed returned at the potentially dangerous score of 3-2, 30-30, to calmly produce an ace and a forehand winner.
Breaks of serve were swapped before Williams took the set in 47 minutes with a backhand and a scream.
Sharapova was looking at another one-sided defeat when facing break points early in the second, but showed why she is a five-time Grand Slam champion.
She served her way out of trouble and managed to cling on in a set in which Williams hit 15 aces and won almost 90% of first-serve points.
A gripping contest developed, with Serena escaping at 3-2, 0-30 thanks to three aces and a service winner.
Another game of three aces led to the American being called for hindrance after shouting "Come on" before the point had finished, and she mockingly mouthed "calm down" to herself after another winner soon after.
Sharapova would not give in, saving a match point with a screaming forehand winner to make it 5-5, and seeing off a second in the tie-break behind a bold second serve.
Williams had a third opportunity, however, and after an apparent ace was called a let - much to her disbelief - she clinched it with another unplayable serve.
"I've not beaten her for a long time, but I love every time I play her as she is the best and you want to play against the best," said Sharapova.
"I gave it everything. I love playing in the Rod Laver Arena, I've had some of my best memories and toughest losses but that is the life of a tennis player."
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