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.
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.