Wade, one of the pre-tournament favourites, lost 4-2 to the No.?47-ranked player in the final game of a dramatic day in London.
Having lost the first set, Wade was thrown out of his stride by Suljovic's methodical style and soon found himself 2-1 behind. Suljovic missed two shots at double six to move 3-1 ahead, allowing Wade back in at 2-2, but he took the fifth set despite missing seven doubles in an earlier attempt to clinch it.
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Hide AdEarlier in the evening, Simon Whitlock was in blistering form as he crushed Denis Ovens 4-0.
The Australian had a checkout of 136 and was in ruthless form on the doubles as Ovens won just two legs.
In the night's other game, Wes Newton hammered Brendan Dolan 4-0. Earlier in the day, Mark Walsh beat Alan Tabern 4-3 in a thrilling duel that lasted almost two hours.
The other game of the afternoon session saw Vincent Van Der Voort secure a last-16 berth as he beat Wayne Jones 4-2.