The Swede will next play Germany's Philip Petzschner, who upset 31st seed Tipsarevic 6-4 6-0.
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There were also victories for Serbia's Janko Tipsarevic, Spain's number four seed David Ferrer and Canada's Milos Raonic.
The German defeated world No. 37 Janko Tipsarevic of Serbia 6-3 6-7 (6-8) 7-6(8-6) in the first round.
But more errors allowed Tipsarevic to race through the tie-breaker 7-3 and leave Murray with an uphill task.
The Frenchman went through after beating Serbian third seed Janko Tipsarevic 6-4 7-6 (12-10) in the second semi.
Sweden's Robin Soderling progressed in straight sets as he overcame the serve of Janko Tipsarevic 6-3 7-6 (7-5).
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.
The Australian Open champion's fellow Serbian Janko Tipsarevic, the seventh seed, will next face French No. 11 Gilles Simon.
His opponent Wednesday will be No. 11 Gilles Simon, who rallied past No. 7 Janko Tipsarevic, 5-7, 6-2, 6-2.
But Tipsarevic took the fourth game to trigger a burst of fine tennis.
If Djokovic can win, then the final rubber between Stepanek and Tipsarevic will decide who progresses to face the French.
Berdych will now need to defeat Ferrer in his final tie to qualify, and hope that Djokovic slips up against Tipsarevic.
Tipsarevic had knocked out fellow Serb Djokovic a day earlier, taking advantage of his compatriot's dislike of the blue clay surface.
World No. 9 Tipsarevic finished the six-man tournament in fourth place after losing 7-6 (7-4) 6-2 to fifth-ranked Ferrer in Saturday's playoff.
Last year Roddick was knocked out in the second round by Janko Tipsarevic, but insists he is better prepared this time.
Roddick lost to Janko Tipsarevic, while Djokovic went out to Marat Safin.
However, the Scot's preparations suffered a blow on Wednesday when he was beaten by Janko Tipsarevic at The Boodles exhibition tournament in Buckinghamshire.
Murray again broke early in the second thanks to a sublime crosscourt backhand but, just as in the first set, Tipsarevic fought back.
Djokovic will meet Nicolas Almagro in the final after the Spaniard came from a set down to defeat Janko Tipsarevic 2-6, 7-6, 6-2.
If he wins, Nadal will then take on his 12th-seeded compatriot Nicolas Almagro or Serbia's world No. 8 Janko Tipsarevic in the quarterfinals.
Janko Tipsarevic gave the 2010 winners an unassailable 3-1 lead with a 6-2 7-6 7-5 win over Michael Ryderstedt in the opening reverse singles.
Dimitrov is also on a roll, having followed up his opening victory over world No. 10 Janko Tipsarevic by beating Germany's Florian Mayer 6-2 6-4.
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According to ITF statistics, Tipsarevic was among the minority of players who had to provide samples both in competition and outside of it in 2012.
Having squandered one set point on the Tipsarevic serve, the set was left at 5-2 when the black clouds finally burst and play was suspended.
In other matches, fourth seed David Ferrer beat Ivan Ljubicic 3-6 6-2 6-1, and fifth seed Marin Cilic defeated Janko Tipsarevic 2-6 7-6 (7-3) 6-4.
The Croatian defeated fourth-seeded Serbian Janko Tipsarevic 6-1 6-3 on Saturday, while Wawrinka beat Israeli fifth seed Dudi Sela 6-4 2-6 7-5 in the other semifinal.
Ferrer is fighting for a semifinal place with Juan Martin del Potro, who beat Tipsarevic 6-0 6-4 in Thursday's late match to end the Serbian's hopes.
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He finally triumphed 6-7 (4-7) 6-3 6-4 in two hours and 35 minutes against the 27-year-old, who beat Serbian Janko Tipsarevic in another three-set match on Friday.
The Serbian defeated Spain's Fernando Lopez 6-3 6-3 and will now face Germany's Tommy Haas in the quarters after he beat Djokovic's compatriot Janko Tipsarevic 6-2 6-1.
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