Unai Emery's side turned the screw following a poor first-half showing and were fully deserving of their victory at Villa Park, despite the Bosnian champions defending stubbornly as well as having chances to steal all three points.
With a view to their West Midlands derby against Wolverhampton Wanderers on Sunday afternoon, Emery made six changes to the XI which dismantled Brighton & Hove Albion last weekend, with the likes of Clement Lenglet and Diego Carlos being handed the opportunity to impress in the hosts' backline.
Looking to build on that success against the Seagulls in the Premier League on Saturday, Villa dominated possession in the first period but never truly threatened to break the deadlock on too many occasions - to the clear disappointment of the Second City crowd.
The Bosnian champions had the first sight of goal in the sixth minute when Mario Cuze broke past the hosts' defensive line on the left flank and spotted Emiliano Martinez off his line, however the winger was unable to keep his chipped effort on target to potentially give Zrinjski a shock lead.
Emery's side continued to keep hold of the ball but failed to break down a stubborn defence, and in the 15th minute Mostar had the best chance of the first period to go ahead in the Thursday night contest, although they were unable to finish effectively.
During their dramatic 4-3 win over AZ Alkmaar a fortnight ago, Zrinjski managed to net four of their five attempts on the Eredivisie side's goal, but such composure was not on show from target man Nemanja Bilbija this time around, who hit his strike straight at Villa's World Cup-winning goalkeeper from a few yards out following a low cross by Mario Ticinovic.
The English side's best opportunity of the first period arrived via fortuitous circumstances, with a hopeful Luca Digne cross deflecting off a Zrinjski defender and subsequently looping high into the Villa Park air - under the gaze of Nicola Zaniolo.
The Galatasary loanee had plenty of time to watch the ball fall from the sky and attempted a bicycle kick from just inside the box, forcing Monstar keeper Marko Maric into a save at full extension in front of an increasingly-frustrated home support.
Clearly unhappy with his team's performance during the opening 45 minutes, Emery made a bold triple substitution during the half-time interval, bringing on Douglas Luiz, Matty Cash and last weekend's hat-trick hero Ollie Watkins at the expense of Leander Dendoncker, Digne and Jhon Duran.
With the aid of some of their star players entering the field of play, Villa commenced the second period in much more threatening fashion, and in the 54th minute the hosts thought that they had been awarded a chance to take the lead from 12 yards out.
Referee Urs Schnyder pointed to the penalty spot after Watkins's header was adjudged to have struck Slobodan Jakovljevic in the arm, however VAR intervened and the Swiss official soon realised at the monitor that the ball had smashed into the defender's face before falling onto his hand.
The disappointment of not being given that penalty did not halt Villa's onslaught of the Zrinjski net, with McGinn and Youri Tielemans among those who forced decent stops from 27-year-old Maric in front of a purring Holte End crowd.
It looked for one moment that Emery's side would have to settle for their second disappointing result of the group stage, however captain McGinn got across his marker from a Cash cross and flicked the ball into the bottom corner, past a helpless Maric who could do nothing to keep his clean sheet in tact.
Villa will be looking to make it six wins from eight in the Premier League on Sunday afternoon when they travel across the West Midlands to face Wolves at Molineux - a venue the Villans have lost at during their last two visits, with maximums points against Gary O'Neil's men potentially enough to take Emery's side level on points with Manchester City.
Zrinjski are currently six points off the top of the Bosnian Premier League despite collecting a very respectable 15 points from their opening seven matches - Krunoslav Rendulic's side host Sloga Doboj on Monday night before the second international break of the term.