Barrett scored a try, set up two others for Julian Savea and Cory Jane and kicked 13 points as last year's beaten finalists advanced to 48 points in the table.
The Waratahs remained on 39 points and neither the 2014 champions nor ACT Brumbies can head off the Wellington-based side ahead of the final week of the regular season.
The worst place the Hurricanes can finish is fifth, the last playoffs spot available in the Australasian group, with the Otago Highlanders (43) playing the Jaguares in Buenos Aires later on Saturday.
Super Rugby
Hurricanes hang tough to make Super Rugby final
30/07/2016 AT 09:48
The Waikato Chiefs (51) lead the New Zealand conference, having demolished the Queensland Reds 50-5 in Brisbane on Friday, one point ahead of the Canterbury Crusaders who thrashed the Melbourne Rebels 85-26 earlier on Saturday.
Barrett scored all of the Hurricanes' first half points with two penalties and a try after a clever kick ahead from winger Jane had turned the Waratahs' defence.
The home side, who struggled to get their hands on the ball, finally managed to put together a number of pick and goes near the ruck with massive winger Taqele Naiyaravoro crashing over.
Waratahs flyhalf Bernard Foley, who had converted Naiyaravoro's try, added a penalty in the third minute following the halftime hooter after the Hurricanes had been penalised three times by Chris Pollock.
The home side moved down field and reduced the gap to 11-10 at the break.
The third penalty had resulted in Willis Halaholo spending the first 10 minutes of the second half in the sin bin and the Waratahs exploited the gap in midfield with Israel Folau crossing to give his side the lead.
Barrett, howver, sparked the Hurricanes recovery, setting up Jane for a try, adding the conversion and then a penalty before his long pass put Savea into space to score and give the visitors a 28-17 lead with around 20 minutes remaining.
The Hurricanes play the Crusaders next week in Christchurch, while the Waratahs head to Auckland to face the Blues at Eden Park.
Super Rugby
All Blacks' Jane, Vito, Savea dropped by Hurricanes for breaking team rules
12/05/2016 AT 06:45
Super Rugby
Naholo back with two tries as Highlanders beat Chiefs
07/05/2016 AT 09:35