Finlay Christie, Nepo Laulala, Ricky Riccitelli, Zarn Sullivan and Mark Telea crossed for the Blues who stretched their winning streak to nine over the outclassed Waratahs in Michael Hooper's final game for the Australian side.
"There's still work to be done, but still pretty happy with that performance," said Blues captain Dalton Papalii.
"They're a good team and it's such a hard competition now... We just knew we had to bring it."
The Blues will likely face the Canterbury Crusaders next in a repeat of last year's final, with the defending champions strongly favoured to beat Fijian Drua as quarter-final hosts in Christchurch on Saturday.
Leon MacDonald's Blues finished third in the regular season but appear to be peaking at the right time.
Their All Blacks forwards bossed the breakdown and their nimble backs were virtually flawless with ball in hand against the Waratahs, who were thrashed 55-21 in the teams' previous meeting at Eden Park.
The Waratahs, thrashed 55-21 in their previous meeting at Eden Park, snatched a try through Ned Hanigan in the third minute from a Blues mistake and led 7-0 in a heady start.
But that was as good as it got for Darren Coleman's team who were then kept scoreless until 10 minutes from the siren when winger Dylan Pietsch ran on to a cross-kick for an easy try.
"It's disappointing," said Waratahs captain Jed Holloway.
"A couple of great men... finished their careers at the club and it's disappointing we sent them out like that.
"They (Blues) made a mess of our breakdown. We paid for it and gave them a couple of easy exits through indiscipline."
The remaining three quarter-finals will all be played on Saturday, starting with the table-topping Waikato Chiefs hosting the Queensland Reds in Hamilton.
The defending champion Canterbury Crusaders then meet playoffs debutants Fijian Drua in Christchurch before the ACT Brumbies host the Wellington Hurricanes in the late match in Canberra.
