The world number nine, whose Wimbledon title defence ended at the quarter-final stage, encountered a major obstacle on his road to redemption when Jo-Wilfried Tsonga dumped him out of the ATP Rogers Cup last week.
But the Scot took that setback in his stride and, despite playing in 63 per cent humidity at the Lindner Family Tennis Center, made light work of Portugal's Sousa, winning 6-3 6-3 in little over an hour.
Murray won the three opening games in less than 10 minutes but Sousa - the world number 37 - finally held after the advantage changed hands numerous times during the fourth game.
There was an exchange of games before Sousa broke Murray for the first time, yet the Scot was not for turning and wrapped up the first set before 40 minutes lit up on the scoreboard.
Although Sousa frustrated Murray at 2-1 in the second set and eked out two more games, the former Wimbledon champion was in cruise control despite the Cincinnati heat and breezed to victory.
He will play the American John Isner - he was runner-up last year and beat Marinko Matosevic of Australia in straight sets yesterday - for a place in the quarter-finals.
Murray said: "I got the win and that's the most important thing. It's very different conditions here this week and a lot of the guys are struggling to control the ball, so I was happy to come through. He [Sousa] is a tough player. He makes a lot of balls and he fights hard so it's a good start."