Gulbis has a reputation as a joker off the court and is rated one of the next generation of players to lead the ATP.
Last year saw Gulbis deliver on that potential, with title wins in Nice and Marseille but he made his biggest statement at Roland Garros, when he overcame Roger Federer in five sets to reach his first grand slam semifinal.
Vesely will have his hands full but will enter the match with confidence after dealing to Brazilian hope Thomaz Belluci 6-3 7-6(4) on day two.
Big-serving Anderson takes on Struff (DS)
Day three begins with a centre court match-up between South African fourth seed Kevin Anderson and German Jan-Lennard Struff.
Currently at world number 16, the big-serving Anderson is looking to carry on his impressive 2014 form that saw him reach the third round of Wimbledon, and the fourth of Roland Garros for the second year in a row. He was also a finalist at both Acapulco and Delray Beach.
The 28-year-old giant will meet a tenacious Struff, who yesterday took care of highly touted Austrian Dominic Thiem.
Bautista Agut returns (DS)
Spanish third seed Roberto Bautista Agut will start his title quest with a centre court clash against Frenchman Adrian Mannarino.
Bautista Agut, on his fourth visit to Auckland, will be looking to improve upon last year's effort that saw him lose in the semifinals to eventual champion John Isner.
He'll need to be on-song to get past Mannarino, who looked efficient dispatching Argentina's Federico Delbonis 6-1 6-1 on Monday.
Kiwis doubles in action (MB)
The last centre court match will be worth staying around for, with Venus and Artem Sitak combining to take on the third seeded Colombian pairing of Juan Sebastian Cabal and Robert Farah. Both New Zealanders have had significant success in doubles over the past 12 months, including grand slam appearances and Sitak also faced Rafa Nadal last week in Doha.
Best of the rest (MB)
There is a doubles fiesta on the outside courts, with five matches across the day . American Donald Young features in the only singles match outside the centre court.