Striker Hogan finished crisply in the 85th minute and then played a large part in Dale's second goal.
His shot was saved well by home keeper Martin Rice but Vincenti followed up to hammer the ball home in off the underside of the bar.
Rochdale had the lion's share of possession and chances in a dour first half of limited opportunities.
Dale's Andrew Tutte fired the first warning shot, forcing Rice to save well with his legs early on as the visitors started brightly.
Rice was again called into action as Tutte's midfield team-mate Matthew Lund forced the Gulls keeper to save well in the centre of his goal.
United countered with Ade Azeez's deflected angled shot forcing Dale keeper Josh Lillis into rare action before central defender Anthony O'Connor's header was headed off the line in the 27th minute.
Hogan's superb mazy run into the box on 64 minutes forced Rice to save well, low down before Dale broke the deadlock late on.