The only goal came 12 minutes in when Sheila Burns found the net to put the home side ahead after Katie Power had pointed for the visitors.
Although Rachael Maloney replied for Cork, points from Sinead Millea had the sides all square at the break.
Orla Cotter and Rena Buckley kept Cork in touch, but it was the unerring accuracy of Sinead Millea that proved decisive.
The second game in Division 1 saw Wexford defeat Dublin on a scoreline of 1-15 to 2-4.
Six minutes into the second half Kate Kelly crashed home Wexford’s goal and although Ciara Lucey found the Wexford net for Dublin’s second goal time was running out. Wexford ran out deserving winners.
In the other group game Tipperary defeated Limerick by 1-15 to 0-4.
Derry had already secured a place in the Division 2 final before they defeated the other Premier side 3-13 to 1-3.
Clare qualified for a meeting with Derry when they had a merited 6-9 to 3-5 victory over Waterford.
Laura Linnane became the heroine of the Clare side in the second half scoring a hat trick of goals. Meanwhile Antrim beat Laois in the only Division 3 game on a scorline of 2-09 to 2-07.