Striker Surridge scored early from the spot and after two Dons goals then leveled proceedings before the break, finishing off a fine team move from the Cherries.
Starting with a similar line-up as had beaten Reading comfortably last week, Stephen Purches's men got off to a flying start when they took the lead from the penalty spot after just five minutes.
Surridge was fouled at the back post as a visiting corner was delivered and the striker confidently took the kick himself, finishing low and in the corner to open the scoring.
The Dons levelled after 12 minutes, however. George Oakley finishing neatly in the area after anticipating Chris Whelpdale's pass forwards.
Wimbledon were ahead on 23 minutes when Toyosi Olusanya controlled well in the area and finished with power, but two minutes later Surridge had his second after a fine team goal.
Worked from the back, Keelan O'Connell was played wide on the right and his low ball in was converted by Surridge to level the score line.
Surridge then struck the under side of the bar with a brilliant free kick with matters square at the break.
Tighter in the second half, Mihai Dobre had a golden chance for the Cherries when he bustled into the box, but with just the 'keeper to beat a sprawling save kept the scores even.
Surridge was soon diving to redirect a header, but chasing his hat-trick the ball rustled only into the side netting.
The high intensity continued to the end but neither side was able to force a winner as the game with a point a-piece.
AFC Bournemouth: Steadman (gk), Jordan, Hobson, Buckley, Harfield, Ndjoli, Simpson (c), Taylor, Dobre, Taylor, Surridge
Substitutes: York, Dennis, Boote, Green, Ofoborh