Barrett was responsible for setting up Cory Jane's try with a long, flat pass, but the All Blacks' wing did well to create room for his dive in the corner.
Pat Lam's Blues were in danger of a thrashing at Newlands - a disappointing follow-up to a good performance in beating the Bulls a week earlier. But with the score 17-3 the Blues rallied through tries to Benson Stanley and Charlie Faumuina before the Stormers eased away again.
A Keven Mealamu calf injury is another issue that Lam, who is already missing Jerome Kaino, Isaia Toeava, Rudi Wulf, Anthony Boric and David Raikuna, must contend with as the Blues travel back to Auckland and prepare to play the Hurricanes on Friday night.
The Chiefs' run continues despite a draw looking the most likely result against the Brumbies in Tauranga. A converted Sam Carter try had the score 22-22 with four minutes left before Jackson Willison scored in the corner which Aaron Cruden did well to convert.
"We came so close. It's not nice to lose in that way," said Brumbies' coach Jake White.
"I thought maybe it was enough to get a draw even though we didn't use our opportunities in the first half, then we ended up losing in the last play of the game."
Sona Taumalolo was his usual irresistible self and scored an inevitable try from close range for the Chiefs, who are third overall on the table with 14 points. They will bank another four points this weekend [24,25/3] as they have a bye and it comes at just the right time for coach Dave Rennie.
"We didn't have the same sort of commitment to the ball on the deck," he said of the win, which has come after victories over the Blues and Crusaders.
"But we've had three very tough games against Kiwi sides and certainly our boys were pretty tired after it."
In Durban, the Sharks fought back from 17-0 to beat the defending champion Reds 27-22 today (Sunday). It was the Reds' first loss of the competition.