And the Scot was not for the benefit, operation six - used to get a second break in the game Dolgopolov seemed to abandon a groin injury.
Giving to Murray the chance for the sentence to serve, and after saving two break points - it correctly on the line.
Open finalist continued his domination in the second row, with no. 15 of the world no response to the Australia.
Murray, who saw Dolgopolov in quarter-final on the road to the final at Melbourne Park last year, resulted in a 4-0-lead in the second series with its mix of aggressive and complicated game.
Dolgopolov showed great spirit, return in the second series, claw, still on the Board of game 5 and paralyzing then Britain, citing a break be clean with a ferocious forehand.
He was once more - two to six and two other stations - close in a game of Murray, but it was also good that the Minie Renaissance for Dolgopolov as the Scot moved to things to do tempo.
Murray was delighted with his victory the perfect way to prepare for the Open of Australia.
He said: "It's a very good start of the year." I started the game well, have a short break at the beginning.
I took my foot on the gas and he kept the pressure.
"I managed to get a break early in the second set, I am very satisfied with the way and I was playing and the way which I blocked the initiative at the top, as I".
In the meantime British was Elena Rezai of Hobart international-1 in the sentences today by seed eighth Camelia Irina Begu of the Romania struck.
Hamilton defend decent in the second series, but could use only two of six breakpoints, won the 21 years of Bucharest a 6 - 2, 7-5 victory.
Begu will face compatriot Simona Halep in the second round.