The all-round strength of Ballymena was too much for Limavady although the score-line may be a bit flattering as the visitors scored a late breakaway try.
Ballymena gradually gained the upper hand and, following a lot of pressure, took the lead with a penalty from Caleb Morrison and six minutes later they scored their first try.
The ball was moved well across the three-quarters before left winger Calum Patterson scored in the corner to make it 8-0. Limavady fought back and although they had the better of the contest for the remainder of the period they were not up playing to their potential. However they deservedly reduced the arrears before the interval.
Out-half Nathan Barr, who kicked intelligently throughout, had just missed with a penalty attempt earlier from the ten metre line but two minutes from the interval he was given a second chance and made no mistake.
Just into the second half, following a line-out, Ballymena drove the home team back over their line and Morrison was successful with the touchline conversion.
The visitors had a 15-3 lead but it was Limavady who gained the better of the exchanges for the remainder of the tie except for the disappointing end.
For the final eight minutes they were encamped well inside the Ballymena '22' but even when the visitors had a prop yellow carded for killing the ball they were unable to penetrate the strong defence.
At one stage the referee stated that the ball was grounded an inch short but they continued to throw everything into attack.
When the ball was moved out to the centre, five minutes into injury time, it was intercepted by Nicholas Sterling who dashed down the pitch to give Morrison a simple conversion.
Morrison had made a considerable contribution to the Ballymena success with his kicking while David Whann made his presence felt in second row.
Ballymena now entertain Friends' in the quarter-final.
Limavady Grammar: C.Crouch, T.Mitchell, J.O'Hara, S.Hull, M.Haslett, N.Barr, P.Wilson, J.Purcell, C.Crampsie, P.Moon, R.Craig, A.Campbell, A.Given, P.Fallows, S.McIntosh, S.Olphert, C.Dixon, D.Boyd, A.Robinson, N.McKeever, A.Blair, A.Robinson
Ballymena Academy: P.Banda, C.Patterson, N.Stirling, C.Delpy, C.Morrison, P.Storey, J.McClelland, D.Geddis, C.Simpson, J.Fleming, M.Galbriath, J.Foster, S.McNabney, K.Galloway, G.Hargy, M.McMurray, J.Andrew, M.Halliday, D.Whann, M.Rea, T.Patton, P.Wallace, P.McKerr, M.Dick, G.Dennison