The two-time grand slam champion had never lost a set against his Portuguese opponent in four previous meetings and needed just 57 minutes to post a 6-0, 6-2 victory.
Murray, who reached the final on his last appearance in Dubai three years ago when he lost to Roger Federer, never had to get out of third gear thanks to 38 unforced errors from Sousa.
The pair met last month in the third round of the Australian Open in what proved another straightforward outing for Murray.
Sousa’s poor record against the Scot seemed to be on his mind from the start, with his errors proving the crucial factor as Murray raced through the opening set in 21 minutes.
It was hard to tell how well the world No 3 was playing because his opponent was being so charitable, and a tally of two winners and 19 unforced errors from Sousa in six games told a sorry tale.
Murray sealed the first set with an ace and then broke serve again at the start of the second.
Sousa finally got on the board in the ninth game however his resistance was fleeting and another break for Murray made it 5-2 before he served out the victory with the minimum of fuss.
Murray was pleased with the way he maintained his concentration throughout against a frustrated opponent.
He said: “The beginning of the second set was a little bit tricky because he was starting to play a bit better and saved a few break points.
“The first set went by very comfortably and then when someone starts to come back into it, that’s when it’s very important to concentrate on the correct tactics and the way that you’re playing.
“Sometimes you go into a match thinking you have less chance of winning. For sure he got off to a very slow start and was very frustrated from even two games into the match, which is quite rare.”
Next for the third seed will be a first ATP Tour meeting with 18-year-old Croatian Borna Coric, who went through in strange circumstances when Marcos Baghdatis retired with cramp at 4-4 in the third-set tiebreak.
Murray played Coric in the Davis Cup two years ago but the teenager has excelled since then and at 84 in the world is the youngest player in the top 100.
Murray said: “He’s obviously one of the young guys who’s going to continue to get better every week with experience.
“He’s going to be making improvements in his game and realising the things he needs to work on if he wants to get to the top of the game.
“He’ll be a tough opponent. He’s had some good wins already against top players.”
Coric’s most high-profile victory came in Basel last October when he beat an admittedly-ailing Rafael Nadal to reach his first tour semi-final.
Murray remains on course for a semi-final clash against defending champion Federer after the Swiss overcame a tricky tie against Spain’s Fernando Verdasco in straight sets. Federer progressed to a quarter-final meeting against Richard Gasquet thanks to a hard-fought 6-4, 6-3 win on Centre Court.
Gasquet, meanwhile, saved a match point on the way to upsetting world No 17 Roberto Bautista-Agut 6-4, 3-6, 7-6 (8/6).
Four-time Dubai winner Novak Djokovic took just 61 minutes to brush aside Andrey Golubev 6-1, 6-2 and seal his place in the quarter-finals.
Djokovic did not offer his opponent any chance to break and the world No 1 will now face Turkish qualifier Marsel Ilhan, who shocked sixth seed Feliciano Lopez with a 3-6, 7-5, 6-3 win on Court Three. Fourth seed Tomas Berdych of the Czech Republic will face Sergiy Stakhovsky in the other quarter-final after both men enjoyed success yesterday.
Berdych beat Italy’s Simone Bolelli 7-6 (9/7), 5-7, 6-0 while Ukrainian Stakhovsky recorded a 6-4, 3-6, 6-4 triumph over Denis Istomin of Uzbekistan.
Berdych became the eighth active ATP player to post 500 career wins after his victory over Bolelli.
“It feels great,” Berdych said. “I need to make sure I keep my body fresh so I can make another 500.”
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