The 29-year-old headed into this evening's match in the French capital soon after top-ranked Novak Djokovic had suffered a surprise defeat to Marin Cilic in his last-eight clash, opening the door for the Scotsman to top the pile this weekend.
Should Murray come out on top in that showdown, with his opponent to be determined later on Friday, he will top the rankings and become the second-oldest person to do so for the first time.
The three-time Grand Slam champion just about took the first set against Berdych following a mammoth tie-break, which he trailed 6-1 at one stage.
After both players held throughout the opener, Berdych powered ahead in the tie but saw momentum slip away as he squandered seven set points, allowing Murray to drag himself level and then get over the line 11-9.
The British ace fared better in the second set, immediately earning the first break of the match in the opening game and then holding to close in on his latest victory in this impressive winning run.
Berdych broke back in the 10th, however, which would ultimately prove to be just a temporary reprieve as a double-fault gave his opponent the chance to regain his advantage - Murray serving out for a sixth win in a row against the Czech, taking it 7-6(9) 7-5 in the end.