The British No1 came back from a set down to avoid an upset against the Latvian 4-6, 6-3, 7-6 (7-4) and book a fourth round clash with American wildcard Mardy Fish.
Murray declared the heat in Cincinnati, which reached 90F, contributed to his struggle, but was clearly delighted with his preparation ahead of this month’s US Open.
“It was very warm and I was struggling to get control,” said Murray, who followed up from his victory in the Toronto Masters last week.
“He was hitting huge. He was comfortable when he was dictating points. I then began to make some first serves and then made sure he would have to play some great tennis to win the tie-break.”