The first frame proved a gruelling encounter, lasting over 40 minutes.
Despite facing a seemingly impossible snooker position – with the cue ball trapped behind the blue near the baulk cushion – Si executed a remarkable escape shot on his third attempt, eliciting a roar from the Ally Pally crowd.
The subsequent frames featured plenty of high-scoring exchanges, with Allen sinking breaks of 111 and 94 in a tactical affair.
The Northern Irishman, who won the tournament in 2018, skillfully navigated a difficult eighth frame where the reds were positioned awkwardly, before pouncing on a miss by his opponent, finishing the match with a break of 80.
"I played well there, I missed one or two shots in the whole game, I just felt like I got the better of the safety side of it," Allen told Eurosport after the win.
"He's such a dangerous player, you need to keep it tight and I did that tonight.
"These are the events you want to play in, this is one of the biggest events in our calendar and probably the best area we play in in front of amazing fans.
"This is the one you want to do well in."
Allen will go up against four-time world champion Mark Selby in the quarter-finals.