The Barbados all-rounder clouted two massive sixes off one James Pattinson over on his way to a dynamic 69 after lunch at the Sydney Cricket Ground.
Brathwaite smashed Pattinson over cover for his first powerful blow before flicking another off his pads for an effortless six over backward square leg.
But Pattinson had the last laugh, bowling the hulking all-rounder in his next over.
Brathwaite's 69 runs came off 71 balls with seven fours and four sixes and further enhanced his reputation after his 59 on debut during the second Test in Melbourne.
"I'm not satisfied that I didn't carry on to get three figures or firstly to see out the day but I'm still happy in sense that I got my highest Test score."
Brathwaite, who gave the 14,266 bedraggled fans some entertainment on a frustrating stop-start day, said he was disappointed to get out.
"I was very, very upset. Not on the dismissal because I think it was a good nut (ball), but I was upset that once again I got a start and couldn't carry on and one of the main mantras in cricket is that when things are going good you maximise," he said.
==================
Steve O'Keefe, one of two recognised spinners along with
Nathan Lyon in an Australian team for the first time in a decade in a home Test, said there was still time for Australia to get a result.
"I think so. I think there's still a hell of a lot of cricket to go," O'Keefe said."If you can get three days in then that's close to 300 overs.
"Hopefully, if the skipper sees that spin will play a big role then we might get more overs in towards the back end of the match if the wicket keeps spinning, it's spinning already."
There was no further play after tea with large tarpaulins covering the pitch and wicket surrounds.
The West Indies were 248 for seven with Denesh Ramdin on 30 and Kemar Roach yet to score.
"It (the rain) is annoying. It's hard for the guys to continually switch off and get back up," O'Keefe said.
"But we have got loads of good structure around us and support staff and they get us switched on and Smithy (Steve Smith) makes sure that with 10 minutes to go that we're ready and out there to do a job."
The West Indies, who are playing in their first Test at the Sydney Cricket Ground in 15 years, have not won a Test in Australia since 1997.
More rain was forecast for Tuesday.
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