Ultimately, it came down to Wesley using their big runners to break the gain line for Pollock to win instant hero status when he plunged for the whitewash two minutes into injury-time.
It was difficult not to feel a degree of sympathy for St Andrew's, for they had looked the more likely from the platform given by a stunning backline movement.
Right wing Luke de Renzy flew onto out-half Daniel Joyce's inside ball to carve up the midfield and centre Gary Fearon was at his shoulder to take the ball through two defenders for a ninth minute try, converted by De Renzy.
This was all the encouragement St Andrew's needed to keep rolling forward for De Renzy to clip over a 16th-minute penalty when Wesley lost their discipline. Someone had to step up for Wesley. Loose-head prop Adam Garvey was that man. He ploughed through the first line of defence and kept the ball alive for replacement Luke Madeley to ground it in the 29th minute.
The deficit was wiped out entirely when captain Andrew Walsh was on hand for try number two in the 38th minute, centre Tim Hawe completing the turnaround with a conversion to put Wesley 12-10 in front.
There was time enough for dramatic scenes as De Renzy kicked St Andrew's ahead when his penalty from distance grazed the inside of the left upright. The minutes ticked by. St Andrew's were in control of the ball entering into added-on time. They rumbled around the side, eating into the clock.
But captain Walsh executed a wonder steal in the shadow of his posts. The losers were then penalised for not rolling away, pinged again for offside.
Wesley made the most of the territory they were given, blindside Pollock muscling his way to the line to set up a Vinnie Murray final against the winners of this afternoon's clash between St Gerard's and Mount Temple.
SCORERS: Wesley College 17 (S Pollock, A Walsh, L Madeley try each; T Hawe con); St Andrew's College 13 (G Fearon try; L de Renzy 2 pens, con).
St Andrew's: L Boorman; L de Renzy, M Kirk, G Fearon, S Keenan; D Joyce, D Hide; A Porter, A Brady, R Brady, M Robinson, A Guy, L Kavanagh, B Ingram, G Jones (capt). Replacements: J Cassidy for Guy, G Beere for Fearon, both 45 mins; D Higgins for R Brady 54 mins; R Bradley for Kavanagh 56 mins; J Balbirnie for Hide 59 mins.
Wesley College: M Strong; G Hughes, R Bracken, T Hawe, A McDonnell; J O'Donovan, A Copeland; A Garvey, J Hopkins, K Sweeney, J Pratt, C Douglas, S Pollock, A Walsh (capt), D Kelly. Replacements: L Madeley for Strong 20 mins; P Cullen for Sweeney 54 mins; S Dalby for Douglas 64 mins.
Referee: A Lynch, Leinster Branch.