Harris laid the groundwork with 56 from 38, before Styris (43 from 20) took three sixes from one Bruce Martin over to up the ante. Mitchell (42 from 19) finished it off and left Auckland with some work to remain alive in the competition.
And it was work their batsmen - aside from Craig Cachopa (47 from 30) - never looked like completing, reaching their allotment nine down and still 40 runs short.
Devcich was the key weapon for the Knights, taking the first three wickets to fall, while Black Caps Trent Boult and Ish Sodhi also snared three scalps each.
In the day's other match, Canterbury kept alive their playoff hopes after Dean Brownlie hit 86 from 36 to help his side to victory over Wellington.
Coming into the contest at Hagley Oval, both sides needed victory to remain realistic contenders to finish in the top three playoff positions.
While Wellington, having completed their 10 games, are now left relying on other results, Canterbury have Brownlie to thank for keeping their fate in their own hands. The Wizards are level with Wellington in third spot and will be assured of qualifying with a win over Northern Districts on Tuesday.
After James Franklin won the toss and elected to bat yesterday, his side's innings never got off the ground as Rob Nicol removed both openers in the seventh over. The opening partnership of 47 was Wellington's best, with regular wickets preventing the visitors from finding position to accelerate the scoring.
Franklin chimed in with 43 off 26 balls later in the innings but the Firebirds' total of 154-6 never looked imposing against a heavy-hitting Canterbury lineup.
After Nicol went cheaply in the second over, Canterbury cruised to the target for the loss of two wickets and with more than five overs to spare. George Worker and Brownlie combined for a 119-run stand for the second wicket, recovering from the early setback and winning the match with boundaries.
Brownlie, in particular, seemed in a hurry, perhaps aware of the role net run rate could play with five teams still in the running for the finals but none yet certain of their place.
The former Black Cap needed only 36 balls for his 86 runs, with five sixes and 11 fours. He eventually fell late in the chase but Worker (53no) saw Canterbury home.