Selby (pictured) opened up with a break of 91, with three further half-century clearances leaving him seemingly on the verge of a comfortable victory at 4-2.
However, Welshman Day delighted the home crowd as he recovered with runs of 67 and 88 to set up a decider, which Selby took 83-0.
“I was sitting there at 4-4 and thinking about how I’ve never been behind in this match,” the runaway world number one told worldsnooker.com.
“I hoped to get that one frame and pull away to the next round and that’s what happened.”
Selby faces Marco Fu in the next round and is expecting a hard battle.
“He’s a great player, scores well and tough to beat. But I’m looking forward to it. I’m off until Thursday night now so I’ve got a few days off to keep practicing and get focused.”
Hong Kong's Fu breezed past Scot Anthony McGill 5-1.
McGill, winner of last month's Shoot Out, won the opening frame with a run of 87 but Fu the took charge with breaks of 94, 53 and 56 taking him through.
In Tuesday's late matches, world number three Judd Trump recorded the tournament's highest break of 132, as well as other beaks of 63, 50, 73 and 63, as he defeated Mark King 5-2.
He will next meet Ronnie O'Sullivan in the last eight on Wednesday evening, while Australian Neil Robertson coasted past Barry Hawkins 5-0.
The left-hander stroked in breaks of 65, 83 and 123 in an emphatic win.
The 16-man tournament, with a £125,000 first prize, is the penultimate event before the seeding cut-off falls for the World Championship.
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