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Serena, 35, won 6-4 6-4 to pass Steffi Graf in the all-time list of major winners since the Grand Slams accepted professional players in 1968.
The American regains the number one ranking from German Angelique Kerber.
Australia's Margaret Court, with 24, is the only player still ahead of Serena in terms of Grand Slam singles titles.
"Congratulations Serena on number 23," said Venus, who at 36 is the oldest Australian Open finalist in the Open era.
"I have been right there with you, some of them I lost right there against you. It's been an awesome win.
"I'm enormously proud of you, you mean the world to me. I, God willing, would love to come back. Thank you for all the love."
Serena paid tribute to her sister, who was playing her first major final for eight years, saying: "There's no way I would be at 23 without her. There's no way I'd be at one without her. She's my inspiration.
"She's the only reason I'm standing here today. She's the only reason the Williams sisters exist. Thank you for inspiring me. Every time you won this week, I felt like I got a win too."
Serena went into the match as a strong favourite, but the tension was apparent as early as the third game when she smashed a racquet in frustration, receiving a code violation.
She had broken serve in the first and third games only to hand the advantage straight back each time, three double faults inexplicably littering a desperate game for 2-2.
It was clear the six-time champion was struggling to settle, with 13 unforced errors in the opening five games, while elder sister Venus kept her under pressure with some deep hitting.
The decisive move of the set came with a superb drop volley followed by a thumping forehand winner from Serena to break for 4-3, and this time she managed to consolidate on serve.
In contrast to the opening stages, the following nine games went with serve - Venus recovering superbly from 0-40 early in the second set - but it was Serena who was creating the chances.
She finally capitalised on her sixth break point of the set with a brilliant return to lead 4-3 and followed it up with her best service game of the match for 5-3.
The crowd on Rod Laver Arena had been backing Venus from the beginning as she tried to win a first major title for eight years, and all the more so as defeat loomed and she appeared to struggle physically.
There was a huge cheer when she held serve to force her sister to serve out the match, but Serena recovered from 15-30 to earn match point and fell back on the court in celebration as her sister sent the ball floating wide.
Saturday's final was the 28th instalment of the sisters' on-court rivarly, which began at the Australian Open back in 1998, with Serena now 17-11 ahead and 7-2 up in Grand Slam finals.
Venus, who turned professional in 1994 and has won five Wimbledon and two US Open titles, insisted she was not too disappointed after reaching her first major final since 2009.
"No, because I guess I've been here before, "she said. "I really enjoy seeing the name 'Williams' on the trophy. This is a beautiful thing."
Russell Fuller, BBC tennis correspondent:
Perhaps the most remarkable thing about Serena Williams is the length of time she has been winning Grand Slam titles. The first came on 11 September 1999 in New York; the 23rd on 28 January 2017 here in Melbourne.
The match itself will quickly be forgotten; but never the achievement. Richard Williams used to beg tennis clubs to part with their old balls when he started to put his daughters through their paces in the Los Angeles district of Compton, and now Serena has more Grand Slam singles titles than anyone who has ever played the game, with the exception of Margaret Court.
Williams is now just one behind the Australian - who was watching on the Rod Laver Arena - and in the view of the 18-time Grand Slam champion Martina Navratilova, it is a record she could "shatter" before her playing days are done.
Billie Jean King on Twitter: Congrats @serenawilliams on your 23rd major title and return to the top of the @WTA rankings. You are a history maker and a trailblazer.
Martina Navratilova on Twitter: unbelievable - Serena does it again - what an amazing record!
Angelique Kerber on Twitter: Congrats to @serenawilliams for this amazing achievement!!! What a historic final- both are true champions @Venuseswilliams
Pat Cash on Twitter: Serena Williams continues to make history with her 23 GS. Just amazing! Further solidifies her place among the greatest sports people ever
Serena Williams beat sister Venus in straight sets to win her seventh Australian Open and an Open-era record 23rd Grand Slam singles title.