The eighth seed always looked in control of the contest breaking his opponent's serve three times in total while holding his own serve throughout the match which lasted 72 minutes..
Murray's reward for his victory is a clash against 11th seed John Isner. The top-ranked American and 11th seed blasted his way into the third round firing 16 aces on way to 6-3 7-6 (1) win over Australian qualifier Marinko Matosevic.
If Murray can negotiate that test he is in line to face second seed Roger Federer in the quarter-finals.
"I hit the ball well from the back of the court today," said Murray, who has twice hoisted the trophy in Cincinnati.
"I was able to control the ball well. That was, for me, the most pleasing thing about the match today, because I have seen a lot of the players have struggled so far."
Murray has struggled for form this season and is still hunting his first title since he won Wimbledon in 2013. However, he has a good record in Cincinnati – winning the event in both 2008 and 2011.
Britain's other representative in the draw is out though with James Ward crashing to a 6-2 6-2 defeat at the hand of Julien Benneteau.
Federer outlasted Canada's Vasek Pospisil 7-6 (4) 5-7 6-2 to claim his 300th Masters Series win and reach the third round.
Back in action after losing to Jo-Wilfried Tsonga in the final of the Rogers Cup in Toronto on Sunday, third-ranked Federer appeared sluggish at times as he struggled to tame the 46th-ranked Canadian.
With the victory the second seeded Swiss, a five-time champion on the Cincinnati hard courts, becomes the first player to reach 300 wins in the ATP Tour's elite Masters 1000 events.
The match began with a tight opening set that saw neither player able to capitalise on break chances, Federer eventually winning the tiebreak on a forehand error by the Canadian.
Pospisil, winner of the Wimbledon doubles title with American Jack Sock, battled back to take the second but a focused Federer wasted no time taking charge in the third with an early break on way to clinching the milestone win.
The day featured a pair of early upsets with Taiwan's Lu Yen-hsun shocking fourth seeded Czech Tomas Berdych 3-6 6-3 6-4 while Poland's Jerzy Janowicz knocked off Bulgarian seventh seed Grigor Dimitrov 6-4 3-6 6-3.
The world number 23 gave his 18th ranked opponent a hard-court lesson, winning 80 per cent of his first serves on his way to victory, setting up a date with Federer in the third round.
Fifth seed Milos Raonic of Canada made light work of American wild card Robby Ginepri 6-2 6-2 but ninth seed Ernests Gulbis saw his tournament end at the hands of American Steve Johnson 6-4 6-4.
Other seeds to survive included Marin Cilic, David Ferrer, Fabio Fognini and Tommy Robredo.
Cincinnati Open results
5-Milos Raonic (Canada) beat Robby Ginepri (U.S.) 6-2 6-2
Steve Johnson (U.S.) beat 9-Ernests Gulbis (Latvia) 6-4 6-4
6-David Ferrer (Spain) beat Philipp Kohlschreiber (Germany) 6-7(4) 7-6(4) 7-6(4)
14-Marin Cilic (Croatia) beat Fernando Verdasco (Spain) 7-6(6) 7-6(5)
2-Roger Federer (Switzerland) beat Vasek Pospisil (Canada) 7-6(4) 5-7 6-2
15-Fabio Fognini (Italy) beat Lleyton Hewitt (Australia) 6-1 6-4
11-John Isner (U.S.) beat Marinko Matosevic (Australia) 6-3 7-6(1)
16-Tommy Robredo (Spain) beat Sam Querrey (U.S.) 6-2 6-4
Julien Benneteau (France) beat James Ward (Britain) 6-2 6-2
Jerzy Janowicz (Poland) beat 7-Grigor Dimitrov (Bulgaria) 6-4 3-6 6-3
Lu Yen-Hsun (Taiwan) beat 4-Tomas Berdych (Czech Republic) 3-6 6-3 6-4
Mikhail Youzhny (Russia) beat Andreas Seppi (Italy) 6-3 6-4
8-Andy Murray (Britain) beat Joao Sousa (Portugal) 6-3 6-3
- Sports & Recreation
- Roger Federer
- Marinko Matosevic
- John Isner