Granollers, 39, and Zeballos, 40, had lost three previous major finals together but finally secured their first victory with a 6-0, 6-7 (5/7), 7-5 win.
Granollers had finished on the losing side in each of his previous five doubles finals, including at Roland Garros in 2014 with former partner Marc Lopez.
Salisbury fell short in his bid for a fifth Grand Slam triumph in men's doubles after winning four times with Rajeev Ram. Skupski won at Wimbledon in 2023.