VIDEO: Waratahs head to Durban 'full of confidence'
A Ned Hanigan try at the death sealed the victory for the home side after a seesaw battle throughout the 80 minutes.
The Waratahs will now face the Sharks in Durban next weekend before flying to Buenos Aires to take on the Jaguares.
"Psychologically for us, it's huge," Waratahs hooker Damien Fitzpatrick said after the win against the Stormers.
"Going to the airport getting on the plane, full of confidence now that we can go 80 minutes. We were probably unlucky not to be winning by that stage.
"We probably left three or four really good opportunities out there and hopefully we can stick those ones.
"Some of the plays that Kurtley [Beale] and Israel [Folau] set up, we were probably unlucky not to get more points."
The Waratahs' performance in the scrums against the Stormers will be a big worry ahead of their clash with the Sharks.
They will also have to do that without veterans Sekope Kepu (suspended) and Rob Simmons (quad) for the clash in Durban.
"I hope the refs go into each game with a neutral decision but they're only human, so we understand we probably haven't showed a dominant scrum [against the Stormers] but next week's an opportunity to go out and change that view," said Fitzpatrick.