AUDIO: High praise for Stormers' 'outstanding' defence
The Cape Town side kept their perfect home record intact as they outscored the Bulls four tries to two at Newlands.
After their terrific start, which saw them race to a 12-0 lead, the home side were forced to overcome a five-point deficit in the second half for the bonus-point win.
The final quarter was an arm wrestle and the Bulls tried desperately to haul in their hosts, but the Stormers' defence stood solid to deny the Pretoria-base side the losing bonus point.
The result means the Stormers move above the men from Pretoria into the fouth place in the South African Conference.
"I am very proud. This game meant a lot to us," Fleck told reporters after the match.
"The defence on our line at stages was outstanding, especially when we were at 14 men [after Ramone Samuels was yellow-carded], they got that advantage and we still defended heroically.
"I thought our maul defence was exceptional. They have a decent maul and they kept coming at us, but credit to our boys, we just kept on knocking them back.
"We really worked hard on that during the week. It hurt us last time when they got that two easy tries at Loftus, but credit to our pack and coaches for sorting that out,"
Fleck acknowledged it wasn't a perfect performance but applauded the side's ability to produce an 80-minute performance.
"We created a few opportunities and for the first time this year, we played for 80-minutes. It certainly wasn't perfect but we needed this win and now we look forward to the Chiefs,"
"If we keep striving for that 80-minute performance, we can put other teams under pressure. We have had to fight incredibly hard over the past couple of weeks. It hasn't been ideal but the team has shown a bit of character now and our game is starting to come together,"
In terms of injuries front, the Stormers captain Siya Kolisi will undergo a scan after twisting his ankle.
However, the captain is confident that the injury is not that serious.