Murray starts US Open countdown with Cincinnati win
Andy Murray of Scotland hits a serve during his match against Joao Sousa on August 13, 2014 at the Linder Family Tennis Center in Cincinnati, Ohio - by Andy Lyons
The British number one, who earned the Midwest title in 2008 and 2011, is searching for his first trophy since winning Wimbledon 13 months ago.
His best 2014 showings have been semi-finals at Roland Garros and Acapulco.
Both of his titles came in finals against Novak Djokovic, the Serbian top seed who has won every Masters 1000 title, apart from Cincinnati.
The 27-year-old Scot whose game has been modest since his January return from back surgery, won his 33rd match of the season as he began his tenth appearance at the event.
Murray, who won his first Grand Slam at the 2012 US Open, improved to 3-0 over the 37th-ranked Souza after winning a match in which he never trailed over 71 minutes.
The former world number two handed Souza his 21st loss of the season in either the first or second round.
The seed advanced on his first match point from his opponent's return long.
Murray ended with three breaks of serve and 16 apiece of winners and unforced errors.