Hearts made it four wins out of four in Group A courtesy of Jamie Walker’s second half strike.
The Jambos came into the game with nine points out of a possible nine, but still needed to win by two goals in order to be seeded for the next draw.
Liam Boyce has started this season the way he left off, scoring in Hearts’ three previous matches and despite playing in a slightly deeper role today, he was the first Hearts player to test Thistle’s goalie, Mark Ridgers.
Receiving the ball on the corner of the 18-yard box, the striker sent a ferocious effort towards goal, but his effort was beaten away by the former Hearts stopper.
The visitors had started well. Inverness were composed when in possession, and looked dangerous at the break in what had been a lively opening 20 minutes.
Hearts came close again just after the half hour. Wallace Duffy left a pass-back short and the returning Gnanduillet was onto it, his left-footed strike was well matched by Ridgers’ left boot, who kept his side on level terms.
Alex Cochrane has quietly gone about his business since joining the Tynecastle side, but he came up with a crucial block ten minutes before the interval.
Tom Walsh was picked out at the back post by Shane Sutherland, where he brought the ball down perfectly, but his volley was diverted over by the defender, much to the relief of Craig Gordon in the Hearts goal.
Just when it looked like the action was done for the opening 45 minutes Hearts had the best chance of the half. Josh Ginnelly got to the by-line and drilled a low cross in for Pollock. He diverted the ball towards goal only to be denied by Mark Ridgers who dived instantly to his right, preventing the Hearts youngster from scoring his second goal in as many games.
Nine minutes into the second half and Ridgers was called into action again. Ginnelly’s cross from the right was over Gnanduillet but found the onrushing Mackay-Steven whose volley was parried behind.
Hearts were getting closer and from the resulting corner they couldn’t have gone any closer. Cochrane’s low corner was flicked goal wards by Gnanduillet, his effort came back off the near post, but fell to Pollock, who struck the same post with the rebound. Inverness scrambled the ball to safety and somehow remained on level terms.
Peter Haring and Jamie Walker were introduced with 25 minutes to go as Robbie Neilson’s side continued to search for the opening goal.
The deadlock was finally broken after 74 minutes. Gnanduillet had endured a tough afternoon against his opposite numbers, but when he won a vital flick on to find Boyce Hearts had a two-on-one scenario. The Northern Irishman had the awareness to pick out the substitute Walker with a perfectly weighted through ball and Walker did the rest, drilling the ball low into the bottom corner past Ridgers to give the hosts a deserved lead.
Walker nearly scored his and Hearts’ second with three minutes to go. Another Hearts sub, Euan Henderson linked with Mackay-Steven before the ball was squared for the goal-scorer. This time though his effort was somehow kept out by Ridgers as the hosts advantage remained a single goal.
The Hearts number seven was again involved in the final minute of the 90, he was sieved down by his opposite number Michael Gardyne. Due to the scissored nature of the challenge referee Nick Walsh had little option but to wave the red card in the direction of the Inverness winger.
Hearts pressed for a second in the five additional minutes but failed to find a second goal that would see them seeded for the next round. As a result, Hearts have been drawn against Celtic in the round of 16 the tie is to be played at Celtic Park on the weekend of 14-15 August.
Attention now turns to Saturday as Hearts prepare to welcome Ange Postecoglou’s Celtic to Tynecastle in the opening round of the 2021/22 Scottish Premiership.