It's looked set to be another disappointing night for Villa in the Conference League, having lost 3-2 at Legia Warsaw in their opening game.
However, captain McGinn met Matty Cash's cross in the fourth added minute to deliver the win.
The win was no less than Villa deserved and is their first at home in the group stage of a European competition since they beat Ajax 2-1 in the Uefa Cup in October 2008.
Villa had plenty of the ball in the first half but were ponderous in possession and lacked any real fluidity, finding it difficult to break down a well-organised Zrinjski defensive unit.
Sitting deep in a 5-4-1 formation, the visitors from Bosnia-Herzegovina were happy to soak up pressure with the intention to hit on the counter-attack. That approach almost paid dividends when Mario Ticinovic broke and delivered a low cross for Nemanja Bilbija; however, the striker fired straight at Emiliano Martinez.
Nicolo Zaniolo had the best first-half chance for the hosts when he acrobatically met Lucas Digne's deflected cross, but his bicycle kick was saved by goalkeeper Marko Maric.
Villa looked much more dynamic after the break, thanks largely to the introduction of Ollie Watkins, Douglas Luiz and Cash and a change in shape - opting to play with three central defenders and deploying wing-backs to try to claim real estate further up the field.
The chances started to flow for Villa, with Diego Carlos, Ezri Konsa and Youri Tielemans testing Maric.
Just as the game seemed to be heading for a goalless draw, McGinn nodded home to get his side on the board in the competition.
All four sides in Group E have three points and a goal difference of zero after their opening two games.
Consistency has been a problem for Villa this season and this marks the first time they have won back-to-back games since August.
Unai Emery's decision to make six changes from the side that beat Brighton 6-1 in the Premier League on Saturday almost backfired, but he took positive action at half-time to set his team on the front foot.
This game was hugely contrasting to the meeting with Brighton, who pressed high up the field, and here Villa had to bide their time to get in front.
But this was not the first time they have shown character to come strong late in a game this season, having scored twice in stoppage time to beat Crystal Palace 3-1 last month.
The introduction of Watkins, Luiz and Cash was key to Villa's success, with the latter laying on the assist for McGinn.
Villa could have let heads drop after Maric stood firm on several occasions, but they persisted and eventually savoured their reward.
