The Hurricanes outscored the Rebels eight tries to four in recording their fifth straight win at the start of the season.
Winger Salesi Rayasi scored two of the Hurricanes' five first-half tries, the pick of which was Barrett's first on his return from suspension after his red card against the Queensland Reds in early March.
'Canes captain Brad Shields won the ball at the back of the line-out, popped a pass inside to scrum-half TJ Perenara, who put Barrett over midway through the first half.
"It was good to be back. We had a massive challenge, the Melbourne Rebels are a good side and it was a tough night," Barrett said.
"It's a great start, but it's about being consistent every week," he added after the Hurricanes remained the only unbeaten team in the competition.
They made 14 changes from the side which won away at defending champions the Canterbury Crusaders last weekend, but made an explosive start.
At 33-0 down, the Rebels put in a strong finish to the first half when lock Angelo Smith smashed his way over from close range, making it 33-7 at half-time.
The Melbourne side came out strong for the second half in Palmerston North when centre Lukas Ripley spun his way past defenders to touch down after a quick ball from a ruck.
The Hurricanes scored rapid-fire tries midway through the second-half through flanker Du'Plessis Kirifi and Perenara, who darted over to claim his 59th Super Rugby try to stretch the hosts out to 47-14.
Rebels replacement back Mason Gordon marked his Super Rugby debut with his team's third try when they found space out wide.
Barrett scored his second when he finished off a superb flowing attack as the Hurricanes chalked up 50 points.
Their flyhalf Aidan Morgan was faultless with the boot in landing all eight conversions before the Rebels touched down their fourth try late on when hooker Jordan Uelese dotted down.
