The Waratahs fueled the Hurricanes' counterattacking game with poor kicking and missed first tackles, and the match seemed likely to become a rout.
But Beauden's yellow card for a professional foul in the 17th minute sparked the Waratahs to score through Ned Hannigan.
Tries to winger Wes Goosen and lock Mark Abbott boosted the Hurricanes' lead to 33-7 at halftime as they controlled set-pieces and used long passes to pick gaps in the defence.
The Waratahs made a strong start to the second half with tries to fullback Bryce Hegarty and scrumhalf Jake Gordon which slashed the margin to 33-21 after 47 minutes.
Leaumape's second try made the lead 38-21 but the Waratahs continued to improve, and a try to Andrew Kelaway in the 70th cut the lead to 10 points.
The Waratahs ended the match over the Hurricanes line, denied a try which would have given them a bonus point.
Beauden earned his second yellow card, which became a red card, for a tackle in the 79th, which could have yielded a penalty try.
"When we scored that many points in the first half we've got to come out after halftime and be a bit more clinical," Hurricanes captain TJ Perenara said.
Waratahs captain Michael Hooper regretted another poor start which his team was unable to overcome.
"Our fights can't be questioned this year," Hooper said. "We've won the last 40 minutes in most games, barring last week. But the first 20 is an issue for us and it's really frustrating."
Earlier match report, by Campbell Burnes
There was a time when the Hurricanes were all style but low on substance.
The Cullens and Umagas could punish you from anywhere, the loosies could put themselves about, but the tight five were inconsistent in their application.
Those days are gone, and this was exemplified as the third-ranked team in the New Zealand conference, who have played some of the best rugby in the competition, chalked up a more convincing victory over the second-ranked team in the Australian conference than the final scoreline might suggest.
Watch out when they actually perform at full throttle for the full 80 minutes. Or when they bring back the Saveas and Dane Coles. They were irrepressible in the first stanza and disengaged for some of the second, missing out on the bonus point and over-kicking. Some of TJ Perenara's passing was dusty.
We don't often talk about set-piece dominance when describing the Hurricanes. Not because the pack is sub-standard. Far from it. Rather it is often the X-factor players in the backline who hog the inches and headlines. They were again to the fore in this clash. Matt Proctor, Ngani Laumape and Jordie Barrett ran hard at gaps and made metres seemingly at will.
But the pack deserves a rap, as do forward coaches John Plumtree, Richard Watt and Dan Cron.
There was much pre-match chatter about the size and physicality of the Waratahs. But the visitors were put to the sword in the scrums and the Hurricanes pressured their lineout to such an extent they conceded a try to Mark Abbott off an untidy tap-down. Jordie Barrett's try stemmed from a solid lineout drive. Hooker Ricky Riccitelli was in vigorous form around the track and accurate at set-piece. Michael Fatialofa was prominent in the lineout, while the loose trio of Reed Prinsep, who nearly scored what would have a sensational solo try, Callum Gibbins and Brad Shields combined effectively.
Israel Folau was apparently unwell, so he should have stayed in the team hotel, such was his contribution at centre. The Waratahs again had their moments, but not quite enough of them, though they did enjoy a purple patch of 20 minutes in the second spell which yielded three tries amid more starch. Bernard Foley made an influential return at first five.
Laumape nearly scored in the first minute, but did cross the line twice, to bring him to seven tries for the season, equalling Vince Aso. His star continues to rise.
Two months after injury, Vaea Fifita came off the bench for a 25-minute gallop at lock.
Beauden Barrett has a rib injury, which meant he is not kicking for goal, but he ran and passed to telling effect, his step, gas and long pass for Laumape's second try was poetry. However he was red carded due to two yellows for knocking the ball down.
There were, pleasingly, few scrum resets, little recourse to the TMO, and sparse sundry stoppages.
The Hurricanes travel to Auckland to face the Blues next Saturday, while the Waratahs can lick their wounds on the bye week.
Hurricanes 38 (Ngani Laumape 2, Beauden Barrett, Jordie Barrett, Wes Goosen, Mark Abbott tries; J. Barrett 4 cons)
Waratahs 28 (Ned Hanigan, Bryce Hegarty, Jake Gordon, Andrew Kellaway tries; Bernard Foley 4 cons)
HT: 33-7
