Sock grabbed the initiative in the seventh game of the first set, converting his second break point when Sousa netted a volley.
He was constantly putting pressure on the Sousa serve with heavy returns, and served out the set in 34 minutes.
The intensity lifted in the second set.
They traded breaks early in the set, as Sousa got more of a foothold in the match.
The Portuguese showed great resilience, as twice in the set he was trouble on serve.
The pivotal moment came at 5-5, with Sousa down 0-30 and Sock one winner from being at championship point.
But the 27-year-old Sousa held his nerve - winning the game with a second serve ace - then broke the American in the next game when Sock double faulted.
The crowd was willing a third set - and got their wish as Sousa held, taking the set with a precise forehand dragged across his body.
The Portuguese had the momentum, and took a break in the third game of the final set as Sock appeared to be fatigued, feeling the effects of his warm conditions in his first day match of the week.
But the 23-year raised his level, and broke back in the next game.
The pivotal moment came in the eighth game of the third set. After looking so solid for much of the set, Sousa got the wobbles.
Two unforced errors - including a double fault on break point which pinged off the top of the net - handed the initiative to Sock.
The American made no mistake, serving out with aplomb, to seal the match in just under two hours.
