Dalriada adapted better to the very windy conditions as they sealed a victory which was helped by Grosvenor making far too many basic errors at Orangefield.
The Ballymoney side made the more convincing start and were ahead after three minutes when they were awarded a number of penalties before inside centre Ryan Malcolmson dived over for Rory Strang to convert.
Grosvenor came back and started to play some good rugby and their reward was a Sam Purdon try, goaled by Peter Davidson.
In the second half Grosvenor pressurised early on, but they continued to make handling errors, offering their rivals encouragement.
They did go in front with a Davidson penalty, but with seven minutes remaining Dalriada struck when second row Timmy Woods scored for Strang to convert.
It was a closely fought encounter and Grosvenor coach Kyle McCallan was obviously disappointed.
“It has been the same story all season,” said a clearly dejected McCallan.
“We set out to achieve much but, on the day, rarely play to our potential.
“Some players played below par, but I thought prop Michael Allen was strong and No 8 Stephen Marshall was everywhere.
“I'm looking forward to progressing further in the Bowl,” he added.
Dalriada's David Dougherty knew it was going to be difficult assignment when he saw the wind.
“We had a satisfactory game with Ryan Malcolmson earning the man of the match as he won a lot of ball and made a few promising breaks in the centre,” said Dougherty.
“Johnny Allen was also noticeable, while Andrew McWilliams and Adam Pollock were aggressive in the scrums and the back row of Henry Loan and Dave McKeeman worked hard.”