The 25-year-old Barrett, last year's World Player of the Year, was instrumental in the Wellington Hurricanes' 28-24 win over Auckland Blues at Eden Park on Saturday, scoring one try and setting up their other three.
New Zealand Herald columnist Chris Rattue said he had seen few better than Barrett, comparing him to All Blacks great Christian Cullen, whose electric pace and vision was credited with changing the role of the running fullback.
"Since I've been watching rugby, since the early '70s, the only player who is on Planet Beauden Barrett is Christian Cullen," he wrote on Sunday.
"He's already a better No. 10 than Dan Carter, apart from kicking, which means the British and Irish Lions are in a lot of trouble."
Gatland brings the Lions to New Zealand in June and July for a 10-match tour, which includes three tests against the All Blacks.
Carter made his test debut in 2003 but truly announced himself on the international stage during the Lions tour of New Zealand in 2015, most notably in the second test.
Carter totally overshadowed opposite number Jonny Wilkinson in the match, driving the All Blacks around Wellington Regional Stadium and scoring 33 points in a performance described as the most complete ever seen by a flyhalf.
In a scrappy game on Saturday, Barrett grabbed the match by the scruff of the neck and his searing pace and ability to exploit space led to all of the Hurricanes points.
He scored his try by anticipating a Blues lineout move that broke down and outstripped Auckland's outside backs to run in untouched from 45 metres out.
Barrett's pace also got him outside the Blues' drifting defensive line to provide Ngani Laumape with his try, while his vision to kick into space and then regather the ball set up lock Mark Abbott's second, and match-winning, try with seven minutes remaining.
Hurricanes coach Chris Boyd said Barrett's influence had been key.
"We talked about that we had to win those big moments and he singlehandedly does that," said Boyd. "And he is regularly responsible for seven or 14 points for us each week."
Blues coach Tana Umaga, who played Super Rugby with Barrett's father Kevin, said the flyhalf was only going to get better as the season progressed.
"He's just unbelievable at the moment and playing with that much confidence and vision, with time on the ball," Umaga said.
"He is the world's best player at the moment and he's still showing that."
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
