It is the first time the Mariners have kept a side goalless since round 21 in February 2018.
The new franchise suffered back-to-back losses for the first time and their first away defeat.
The Mariners’ second win of the season lifts them from last to sixth, one spot and three points behind United.
Central Coast started brightly with Tommy Oar putting an audacious chip just over the bar.
From that point, United created the best first-half chances, with the visitors’ star imports all having attempts. Alessandro Diamanti had a free-kick saved by Birighitti and fired another fierce shot just wide, while Panagiotis Kone blazed over from close range and Ziggy Gordon cleared an Andrew Durante header off the line.
United had further chances after half-time, with Besart Berisha missing one from close range and having another effort saved brilliantly before being replaced just after the hour.
Sam Silvera shot straight at Filip Kurto and Jack Clisby almost doubled the Mariners’ lead, but his long-range attempt was tipped away superbly by Kurto. Birighitti preserved the lead by saving an 80th-minute effort from substitute Max Burgess and Diamanti fired another attempt wide.