A penalty save 10 minutes from time by Brendan Clarke helped to maintain the Saints' unbeaten start to the season.
In a game full of incident and chances, Liam Buckley's side created enough chances to win the game, although the visitors had two great chances late in the game.
The Saints had to reshuffle their starting 11 with the James Chambers, Mark Rossiter and Stephen O'Flynn ruled out due to injury and Greg Bolger suspended.
Darren Meenan who scored the opening goal against Derry last week had a great opportunity to opening the scoring but his effort hit the side netting with McNulty beaten.
SWAI Player of the Month for April, Chris Forrester, trouble McNulty on a number of occasions with long range efforts, but the Cork netminder was equal to them.
As the game was heading towards a scoreless draw, Cork's Tadhg Purcell saw an effort come back off the crossbar and moments later saw his penalty saved by Clarke.
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|10||Galway United FC||23||22|