De Allende scored his team's only try in the first half and broke the defending champion's hearts when he crossed again after the break in Sydney.
Kobus van Wyk and Cheslin Kolbe also scored tries to earn a valuable bonus point for the Stormers, who had lost their last three matches and were without influential captain Duane Vermeulen.
“I'm very proud of my boys,” replacement skipper Juan de Jongh said in a televised interview.
“It's not easy to come to Sydney and beat the defending champions. It was an 80-minute performance and our defence was rock solid.”
The win lifted the Stormers from ninth to third in the standings as the new South African conference leaders, although the Bulls will leapfrog them if they beat the Queensland Reds later on Saturday.
The Waratahs dropped to ninth place and are in danger of missing the playoffs with a tough run of matches ahead.
“We had a really good week, preparation-wise,” NSW captain Dave Dennis said.
“We knew what we were going to face but we just weren't good enough. We started well but we dropped off and didn't stick to our game plan.”
The Australians scored the opening try after 13 minutes when giant winger Taqele Naiyaravoro bulldozed past three defenders to touch down in the corner.
De Allende replied with a try for the Stormers but the Waratahs regained the lead on the stroke of halftime when Rob Horne crashed over and Bernard Foley converted from the sideline.
The Stormers dominated the second half, scoring three unanswered long-range tries, including a spectacular 95-metre effort when Kurt Coleman chip-kicked for Van Wyk to race away to the line.
De Jongh intercepted a Waratahs pass inside the Stormers half and sent De Allende away for this second touchdown before Kolbe sprinted 80 metres downfield to score after the Waratahs again coughed up possession. – Reuters
Original source: Stormers return to winning ways