Earlier Richard Krajicek had survived a nailbiting test against Radek Stepanek to reach the quarter-finals.
Fish claimed his first victory over veteran Czech Radek Stepanek with a comfortable 6-3 6-3 win.
But Janko Tipsarevic overcame Radek Stepanek in a five-set thriller 5-7 6-4 6-4 4-6 9-7 to level the tie.
Despite nursing an injured wrist, the world No.8 trounced Radek Stepanek 6-4 6-4 6-2 at the Parque Roca stadium.
Jurgen Melzer reached the final of the Memphis hard-court event on Saturday, beating Czech third seed Radek Stepanek 6-4 3-6 6-3.
Petra Kvitova, the defending Wimbledon champion, plans to play with fellow Czech Radek Stepanek, a strong singles player and a doubles expert.
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Meanwhile, top seed Andy Roddick will play defending champion Radek Stepanek in Sunday's men's final at the Pat Rafter Arena.
Murray will play Radek Stepanek after the Czech beat American John Isner 6-4 6-7 6-3 in a showdown of the big servers.
In the men's event, Czech second seed Radek Stepanek booked his last four place with a 7-6 6-1 win over American Wayne Odesnik.
Yan, ranked 465, stunned world number 30 Radek Stepanek in round one but Murray, who was given a first-round bye, proved far too strong.
Also advancing were No. 22 Fernando Verdasco, No. 28 Marcos Baghdatis, the 2006 Australian Open runner-up, No. 31 Radek Stepanek and No. 32 Julien Benneteau.
Radek Stepanek and Tomas Berdych sealed the Czech Republic's win over Croatia with a 6-1 6-3 6-4 victory over Marin Cilic and Lovro Zovko on Saturday.
Chinese wild card Bai Yan , ranked 465th in the world, set up a meeting with Andy Murray after upsetting world number 30 Radek Stepanek 6-4 6-4.
The Czech Republic are through to the quarterfinals after Tomas Berdych and Radek Stepanek beat Italy 's Daniele Bracciali and Potito Starace 6-3, 6-4, 6-2 in Ostrava.
Radek Stepanek celebrated his first call-up to the Czech Republic's Davis Cup team with a straight sets win over compatriot Jiri Novak at the Milan Indoors event.
Spain's Alex Corretja takes on compatriot David Sanchez while second-seeded German Rainer Schuettler meets Belgian Christophe Rochus and Czech Radek Stepanek, the eighth seed, faces Swiss Michel Kratochvil.
His next opponent, Radek Stepanek, is in doubt after suffering a knee injury during his 7-5 7-5 3-6 4-6 6-4 third-round win over Spanish 16th seed David Ferrer.
Thirteenth seed Radek Stepanek beat former world number one Juan Carlos Ferrero 6-3 6-0 in the first round on Monday, while 16th seed David Ferrer beat Richard Gasquet 6-4 6-3.
Former world No. 8 Melzer followed up his semifinal victory over American top seed John Isner and his earlier win over former finalist Radek Stepanek to claim his fourth ATP title.
Czech 29th seed Radek Stepanek crashed out 7-5 7-5 6-3 against French world No. 81 Nicolas Mahut, who will likely face Djokovic in round three if he overcomes Japan's Tatsuma Ito.
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Sixth seed Del Potro went down 6-4 7-6 to Radek Stepanek of the Czech Republic to make an early exit to the ATP event, while Jo-Wilfried Tsonga of France also crashed out.
Radek Stepanek and Tomas Berdych defeated Nenad Zimonjic and Ilija Bozoljac 6-4 6-2 7-6 (7-4) in a match which lasted two hours and 23 minutes on the clay at the O2 Arena.
In the quarterfinals, they routed Leander Paes and Radek Stepanek, a new team that twice beat the Bryans in straight sets on hard courts earlier this year, including in the Australian Open final.
Goffin stunned Czech 23rd seed Radek Stepanek in the first round proper, then beat more experienced opposition in veteran Frenchman Arnaud Clement -- playing his home tournament for the last time -- and Poland's Lukasz Kubot.
World number one Rafael Nadal will face Florent Serra in the second round after the Frenchman beat Guillermo Canas, and there were first-round wins for Radek Stepanek, Ivan Ljubicic, Philipp Kohlschreiber, Robin Soderling and Andy Roddick.
Latvia's Gulbis, seeded 24th, lost in straight sets to Jeremy Chardy , 28th seed Radek Stepanek lost 6-4 6-2 4-6 6-4 to Julien Benneteau and 30th seed Juan Monaco was sent packing by Canada's Peter Polansky in straight sets.
In the other semifinal, Argentina's hopes of winning a first Davis Cup suffered a setback in Buenos Aires as Tomas Berdych and Radek Stepanek of the Czech Republic beat Carlos Berlocq and Eduardo Schwank in the doubles match on Saturday.
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