Bolat rose high five minutes into injury time to nod home after Jeremain Lens had grabbed the lead for the Dutch visitors in the 42nd minute when he latched on to a cross from Sebastien Pocognoli to side-foot the ball into the bottom corner.
Liege's last-gasp victory left them third in Group H on five points, one ahead of Alkmaar who finished bottom and will play no more European soccer this season.
Arsenal topped the group, despite a 1-0 defeat at second-placed Olympiakos Piraeus who join the Londoners in the last 16 of Europe's top competition.
"We ran, we struggled and in the end we got an historic goal. It's good for the history of football, I think," Standard Liege coach Laszlo Boloni told Reuters.
Wednesday's game in Liege was Alkmaar's first under Belgian national coach Dick Advocaat, who took over for the remainder of the season on Tuesday following the sacking of Ronald Koeman.
The home side deserved their point as they dominated the game for the most part and struck the woodwork on three times in the first half.
Milan Jovanovic hit the crossbar with a free-kick after a quarter of an hour before striking the post with another shot from the edge of the box soon afterwards.
Igor De Camargo's spectacular overhead kick just before the break also came back off the post to deny Liege a well-deserved equaliser after Lens had popped up to put the visitors ahead.
Liege pressed in the second half and went close on a number of occasions until Bolat popped up at the opposite end of the pitch to send his side into Europe's second-tier competition.
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