The world No.9, whose Wimbledon title defence ended this year at the quarter-final stage, encountered a major obstacle on his road to redemption last week when Jo-Wilfried Tsonga dumped him out of the Rogers Cup in Toronto, but he bounced back in Cincinnati.
Although the match was played in 63% humidity at the Lindner Family Tennis Center, Murray made light work of Sousa, winning 6-3, 6-3 in little more than an hour.
Murray won the three opening games in less than 10 minutes but Sousa, the world No.37, finally held serve after both players had several game points in the fourth game. There was an exchange of games before Sousa broke Murray for the first time, but the Scot responded by wrapping up the first set inside 40 minutes.
Sousa was able to frustrate Murray at 2-1 in the second set and the Portuguese eked out two more games, but the two-time grand slam tournament winner was in cruise control despite the heat and breezed to victory. He will next play the giant American John Isner, who reached the final last year and saw off Australian Marinko Matosevic in straight sets yesterday.
"I got the win and that's the most important thing," said Murray. "It's very different conditions here this week [compared to Toronto] 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."
Murray might have been joined by his Great Britain Davis Cup team-mate James Ward in the last 16, but it was not to be. The English qualifier, who had upset Spain's Guillermo Garcia-Lopez in the first round, fell to defeat against Julien Benneteau of France in straight sets and missed out on a tie against Jerzy Janowicz.
Ward's service let him down against Benneteau, the world No.41, who needed just one hour and four minutes to win 6-2, 6-2.
Janowicz, beaten in the semi-finals at Wimbledon 14 months ago but who has dropped out of the world's top 20 this year, was a surprise 6-4, 3-6, 6-4 winner over Grigor Dimitrov, the No.6 seed from Bulgaria, yesterday. Tomas Berdych, the fourth-seeded Czech, lost 3-6, 6-3, 6-4 to Lu Yen-Hsun of Chinese Taipei.
On the sidelines already were Jo-Wilfried Tsonga, last week's winner in Toronto, and, in the Sony Ericsson WTA Tour women's event, the Wimbledon champion Petra Kvitova and Venus Williams.
Tsonga was trounced 6-1, 6-4 in the first round by the redoubtable Russian Mikhail Youzhny, a player who followed up yesterday with a 6-3, 6-4 defeat of the Italian Andrea Seppi.
Venus Williams, who reached the final in Montreal last week by beating her sister Serena for the first time in five years, went down to the Lucie Safarova. The Czech player was a Wimbledon semi-finalist last month.
Meanwhile, Kvitova, who beat her fellow countrywoman at Wimbledon, was edged out 6-2, 7-6 (7-2) by Elena Svitolina, the 19-year-old Ukrainian who is the youngest player in the world's top 35.