The Cape side showed grit at a sold-out DHL Stadium, edging past their rivals 13-8 to extend their unbeaten run in the URC this season.
With the derby now behind them, attention has shifted to Europe, where the Stormers prepare for Round Three of the Champions Cup against Harlequins this weekend.
"It was a very tough game this past weekend, a lot of sore bodies out there, but business carries on as usual for a massive game that awaits us in London," said Hlungwani.
"We want to make sure we're ready, and we will be ready come Sunday."
Hlungwani highlighted the importance of set-piece efficiency after the Stormers dominated the lineout battle against the Bulls, winning 18 throws, with mauls forming a major part of their attacking platform.
"Obviously they're having a bit of a tough time in the Premiership, but they're always really tough when you play them, especially at The Stoop," he added.
"Previously when we went there, I think we picked a bit of an inexperienced team but this time we feel like our guys have gained enough experience, especially the guys who played there the last time, to go and challenge hard and win this game if we can.
"But it's something we're really looking forward to – they are a tough team especially at home, but it's something we'll be ready and prepared for."