The 46-year-old Englishman's feat in the second frame of the match continued his fine run of form after he had scored a rare 146 clearance in the final frame of his fourth-round win over Daniel Wells on Thursday.
And the world number 31, bidding for his second career ranking title win after clinching the Gibraltar Open last year, fired three more half-centuries including a match-clinching 86 against Wakelin.
Fresh from winning last week's Snooker Shoot-out, Wakelin had edged favourite Neil Robertson in a final-frame decider in their last-16 clash earlier on Friday.
Milkins will face Ali Carter in the semi-finals after the Essex veteran recovered a 3-2 deficit to beat rising Chinese star Pang Junxu 5-3.
Jack Lisowski was forced to battle to keep his hopes of a long-awaited first ranking title alive as he beat another Chinese player, Xiao Guodong, by the same score.
Lisowski opened with breaks of 98 and 54 but lost the next three frames before rallying with a break of 78 to level and ultimately easing over the line.
Kyren Wilson opened with a break of 112 but could not sustain his momentum against Tom Ford, who ran out a 5-2 winner and will play Lisowski in the last four.
