Trump came from 3-0 down to overcome Barry Hawkins in the first round and after Allen’s opening-frame half-century had a two-frame deficit to deal with early on.
But the prodigal potter’s shaky long conversion rate and break building soon picked up and five straight frames were kicked off by a slick 108.
The two free-scoring players contested arguably the match of last season in the UK Championship final, also won by Trump, but this was a tougher affair for the Bristol man who meets Graeme Dott next.
Higgins will take on Ali Carter, who in the earlier session also recorded a 5-0 whitewash, in the quarter-finals.
Day had notched three centuries in the tournament but hardly had the table time against the four-times world champion, who began with a half-century before cruising to a 4-0 lead at the interval.
Higgins could only get to 48 in frame five before having to settle for lesser colours. Nonetheless, he did enough to seal the shut-out and set up an intriguing last-eight clash with ‘The Captain’.
Dott was denied his own whitewash by Stephen Lee’s fifth-frame 60 break, but otherwise strolled through their second-round encounter 5-1.
Two half-tons in the same frame capped a pre-intermission whitewash but the Scotsman had to wait before finally sealing victory in frame six.
And Shaun Murphy held off a Mark King fightback to advance to a meeting with Stuart Bingham with a 5-3 win in the session’s longest match-up.
The 2005 world champion began with a 72 break before outlasting the Essex resident in a 45-minute frame to double his lead.
Murphy was soon 3-0 up but King struck a smashing 112 clearance to give himself hope at the break.
A knock of 55 helped King make it 3-2 but Murphy held firm to take the next, and though King kept battling for a final-frame decider by winning frame seven he was barely given a sniff in the eighth as ‘The Magician’ eventually sealed the win.
Stuart Bingham v Shaun Murphy
John Higgins v Ali Carter
Mark Williams v Joe Perry
Judd Trump v Graeme Dott