In what was an end-to-end affair despite dour Eden Park conditions, a try-happy Blues outfit ran in eight five-pointers to four and appeared likely to cut through a meek Cheetahs defensive line at every opportunity.
All Blacks hopeful Rieko Ioane ran riot, scoring two tries and setting up another, while midfielder George Moala did his Test prospects no harm in a classy display.
Loose forward Steven Luatua also impressed as an all-action blindside.
Despite the bonus-point win, the Blues remain pinned to the bottom of the New Zealand conference, but puts plenty of pressure on the fourth-placed Highlanders ahead of their clash with the Bulls in Pretoria.
It also increases the Blues' chances of sneaking in to the final top eight, as they jet off to Cape Town for a clash with the Stormers.
Despite their reputation for running rugby, the Cheetahs could only find joy through the set piece and nabbed three of their four tries via mauls.
"We struggled a little bit with their driving maul, but outside of that we're relatively happy," Blues captain James Parsons said.
"That's probably the only area of concern - we'll enjoy the small wins (and) celebrate tonight, but we're on the early flight tomorrow."
The two sides traded tries in the opening 20 minutes, as Ioane responded to Francois Venter and Scott Scrafton to Torsten van Jaarsveld.
Akira Ioane then broke a brittle Cheetahs left-edge defence to stroll over and put his side in front in the 23rd minute, before lock Patrick Tuipulotu swirled out of two tackles to motor home 10 minutes later.
The Blues were forced to switch first-fives after the break with Piers Francis limping off for Ihaia West, but kept their foot on the accelerator.
Further tries to Luatua, halfback Augustine Pulu and Rieko Ioane put the result to bed, before a breakaway Melani Nanai score was sandwiched by two mauling efforts from replacement Cheetahs rake Elandre Huggett.
"We knew we had to fire up, not do what we did against the Waratahs (concede late points), score first and make sure we put scoreboard pressure back on," Parsons said.
"I thought we did that quite well, especially exiting our own half."