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After fending off two break points in the opening game, Ruud was the first to break after a number of wayward shots from his opponent.
Though Alcaraz continued to struggle to find the court, he had the opportunity to level in the next game but at break point saw his forehand deflect out off the net cord.
Two further chances followed but Ruud withstood the danger and was rewarded for his resolve when Alcaraz again placed a forehand out of bounds for the double break.
Ruud served out the set to love with an ace, only the second set he had taken from Alcaraz – who hit 18 unforced errors and landed less than 50% of his first serves in the opener.
But the Spaniard reset for the second set, dropping just a single point across his first three service games before breaking for the first time.
He looked to be cruising towards levelling the match but Ruud fought back – earning himself two break back points with a lob on to the baseline, but needing only one as Alcaraz netted a backhand.
As Alcaraz’s level continued to slip, a rejuvenated Ruud – who had been just two points from losing the set – broke again before serving out the win with an ace on his third match point, capping a run of five straight games.
Alcaraz and Ruud are joined in the John Newcombe Group by German Alexander Zverev – a two-time ATP Finals champion – and Russian Andrey Rublev, who play in Monday’s evening session from 19:30 GMT.