The Dutchman - who lost his first encounter to Milos Raonic on Wednesday before beating John Isner the following day - recorded a 6-3 6-7 (1-7) 10-8 triumph against the German on Saturday.
A win for Haase is the perfect confidence boost ahead of the third slam of the season at the All England Club, where he will face 31st seed Vasek Pospisil in the first round.
Haase's best showing at Wimbledon came when he reached the third round in 2011, while Struff - who has never gone beyond round two - starts against Lukasz Kubot, a quarter-finalist 12 months ago.
In Saturday's other contest at the grass-court exhibition event, Spain's Guillermo Garcia-Lopez defeated Kevin Anderson 6-4 7-6 (7-3).
Garcia-Lopez is more of a clay-court specialist, with two of his three ATP titles coming on the red surface, and - like Haase - is aiming to reach round four for the first time.