Barrett put himself in prime position for the All Blacks number 10 jersey with a sublime display in the Victorian capital.
The Hurricanes scored six tries to two in a dominant performance that keeps them in touch with New Zealand conference leaders the Waikato Chiefs.
The Hurricanes are now four points behind the Chiefs on the ladder, with the two teams to meet in Wellington next weekend.
“We’re really looking forward to that so we’ll enjoy tonight and rest up, but we know how much those home derbies mean to us,” Barrett said.
The Rebels, who last week made history by beating the NSW Waratahs in Sydney for the first time, would have gone into the match full of confidence after drawing level with the Brumbies at the top of the Australian conference.
The Rebels held their own in the first 20 minutes and even took an early lead when winger Dom Shipperley scored out wide from a Jack Debreczeni kick ahead.
But the Hurricanes struck back soon after when Victor Vito crossed following a superb break from Barrett up the centre of the park.
A Reece Hodge penalty put the Rebels back in front midway through the half but they held on for barely a minute, a Cory Jane try giving the Hurricanes a lead they never looked like surrendering.
A Barrett intercept under the posts made it 22-8, before fullback Jason Woodward crossed two minutes before the break to send the visitors into halftime with a commanding 29-8 lead.
The Hurricanes continued to dominate in the second half but the Rebels lifted their defensive intensity and it took until the 60th minute for the visitors to score, flanker Ardie Savea crashing over after a wealth of possession.
Barrett then crossed for his second when he brilliantly regathered a charged down kick to race away and score under the posts.
Rebels winger Cam Crawford scored a consolation try right on fulltime, but the home side were well beaten by a rampant Wellington outfit.
“We got what we deserved tonight,” Melbourne captain Nic Stirzaker said.
“We had a bit of an off night and were definitely not accurate in a lot of areas.
“I would like to see the territory stats — it didn’t feel like we were in their half at all.
“The inability to get out of our own half killed us.”