Kenneth Vargas hit a late winner as Hearts came through a difficult encounter at Cappielow to reach the Scottish Gas Scottish Cup semi-finals.
The Coast Rican forward fired home in the 86th minute to secure a 1-0 victory over Morton, who had been denied several times by some impressive Craig Gordon saves.
Hearts began to find their attacking form in the final half hour and Vargas powered home a low angled drive after Beni Baningime drove forward and fed Lawrence Shankland.
The victory seals a second semi-final for Steven Naismith’s side this season and leaves them 90 minutes away from a potential fourth Scottish Cup final in six seasons.
The match pitted two of Scotland’s recent in-form sides against each other. Morton had gone on a 16-match unbeaten run, which took them from bottom of the cinch Championship into the promotion play-off places, before suffering home defeats against Inverness and Dundee United in their previous two matches.
Although manager Dougie Imrie had lost the likes of George Oakley, Iain Wilson and Jai Quitongo since the fifth-round win over Motherwell, former Rangers defender Kirk Broadfoot returned from injury to take his place in the back three.
Hearts had won 12 of their previous 15 games and had Vargas back in their line-up after the attacker missed their victory over Celtic.
Morton signalled their intent to test Hearts in the air when Lewis Strapp hurled an early throw-in into the box from 10 yards inside the visiting half.
Another ball into the Hearts box drew the first chance as Gordon used his frame to block Darragh O’Connor’s header following an Alan Power free-kick.
The away supporters had to wait until the half-hour mark before seeing their team come close – Shankland’s first-time shot on the turn was pushed wide by Ryan Mullen.
Alan Forrest saw two efforts deflected wide and Morton were forced deep in the latter stages of the half, but Gordon had to watch Robbie Muirhead’s free-kick as it bounced into his arms.
Both sides stepped up their attacking threat at the start of the second half.
Morton had some initial pressure, but Hearts midfielder Baningime missed the chance of the game so far when he sent a free header over the crossbar from Stephen Kingsley’s cross.
The home side responded by creating two equally strong opportunities.
Gordon pulled off excellent stops from Jack Baird’s header and Strapp’s effort after the left-back had burst into the box.
Mullen was also impressing in the opposite goal and he produced a diving save from Cammy Devlin’s strike from 18 yards.
The game had the sort of edge expected of the occasion and former Morton loan star Shankland was booked for pushing Strapp to the ground in front of the “cowshed” as the home fans shouted for David Dickinson to wave a red card.
The Scotland striker was being watched by international manager Steve Clarke ahead of him naming his latest squad and he set up Vargas for an excellent chance after initially looking like he might get in behind himself.
Vargas had time to pick his spot from 10 yards, but lifted the ball on to the top of the bar and over.
Shankland then set up Aidan Denholm but the substitute shot straight at Mullen, who trapped the ball between his legs.
The skipper would have a major say in the winner though as he collected Baningime’s pass and allowed Vargas to take over.
