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Lucy Geddes gave them a second-minute lead and Rachel and Laura Johnston put them 3-0 ahead before Lurgan's Kerrie Burns pulled a goal back.
Harlequins join fellow Ulster sides Pegasus and Ards in the top division next season.
Cookstown gained promotion to the men's IHL with a thrilling 4-3 win over UCD.
After going 2-0 down early in the game, goals from Paul Thompson, Keith Black and Ryan Millar put the Ulster side 3-2 ahead only for UCD to equalise.
However, a late Greg Allen strike saw Cookstown home to victory and a return to the top flight after a one-year absence where they will join Ulster clubs Banbridge, Lisnagarvey and Annadale.
It was revenge for Cookstown as 12 months ago their place in the IHL was taken from them by the Dublin side in the play-off match.
In the women's Champions Trophy final, UCD completed a treble of league, cup and play-off success with a shootout win over Hermes-Monkstown while in the men's decider hosts Three Rock Rovers beat Monkstown 2-1.
In Saturday's semi-finals Monkstown had ended the hopes of a treble for Banbridge while Three Rock saw off the challenge of Lisnagarvey, with both games ending in shootouts.
Belfast Harlequins retained their place in the Women's Irish Hockey League with a 3-1 win over Lurgan in Sunday's promotion/relegation decider in Dublin.