Andy Murray could overhaul Novak Djokovic’s top ranking if he wins the tournament and gets favourable results at the Paris Masters at the end of the month.
In Vienna, the three-time Grand Slam champion was tested in his opening game as Klizan produced three break points, but the Scotsman was able to hold before breaking serve himself.
The Wimbledon champion saw out the set in 43 minutes and started the second strongly as he went a break up at the first time of asking, but Klizan later responded by snatching serve to draw the contest 4-4.
The Slovakian’s serve then faltered, but he quickly broke back before breaking the world number two a second time to force a tie breaker, which he edged 7-6.
However, it was merely a blip for Murray, who regained his composure and saw out the deciding set 6-0.
The victory sees the Scot move within touching distance of Djokovic in the world rankings.