Barrett compiled 15 points with the boot while fellow All Blacks TJ Perenara (2) and Julian Savea were try scorers in a 35-19 win at the Suncorp Stadium in Brisbane.
The midfield pairing of Conrad Smith and Ma'a Nonu continues to impress for the Canes and head coach Chris Boyd must think carefully about when to give his All Blacks another week off as part of the agreement with the international side.
Victory for the Canes moved them back on top of the New Zealand conference standings, and the overall standings as well after the Chiefs had momentarily replaced them.
The Waikato-based side had to work hard for a 35-27 victory over the Force in Hamilton, Charlie Ngatai, Hikawera Elliot and Tim Nanai-Williams all going over in addition to a penalty try.
Marty McKenzie, replacing the injured All Blacks fly-half Aaron Cruden, added 15 points with the boot to ensure the win.
The Highlanders opted to rest three All Blacks in Ben Smith, Aaron Smith and Malakai Fekitoa and were punished by the Brumbies in Canberra.
David Pocock grabbed a hat-trick of scores for the Australian franchise, Henry Speight also crossing over in a 31-18 victory that puts a dent in the Highlanders' hopes of making the play-offs.
The Crusaders returned to winning ways on Saturday though as they came out on top in the all-Kiwi clash with the Blues in Christchurch.
Mitchell Drummond, Jordan Taufua, Tom Taylor and Codie Taylor all crossed for the Crusaders while All Black Colin Slade chipped in with a penalty and three conversions in a 29-15 victory.
Richie McCaw was withdrawn in the second half after sustaining a head injury and appears likely to miss the Crusaders' key clash with the Hurricanes next week as a result.
Dan Carter was in action at inside centre but it was winger Nemani Nadolo who again stole the show for the seven-time Super Rugby champions.
Defeat for the Blues leaves them rooted to the bottom of the New Zealand standings and second bottom overall.
Elsewhere the Waratahs edged out the Rebels 18-16 in Sydney, the Lions beat the Cheetahs 34-29 in Johannesburg and the Stormers held off the Bulls 15-13 at Newlands.
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