Hearts slumped to a shock 2-0 Premier Sports Cup defeat at Championship club Falkirk as second-half goals from Ethan Ross and Dylan Tait sent their side into the quarter-finals. Steven Naismith’s side dominated much of the first half at the Falkirk Stadium but were wasteful with their chances, Kenneth Vargas striking the crossbar from close range with one of the most glaring misses. That profligacy came back to haunt the visitors in the second period as Falkirk took control and made their opportunities count. The result was already assured by the time Falkirk substitute Ryan Shanley was shown a straight red card in the final minute. The defeat extends Hearts’ winless start to the season before the first leg of their Europa League playoff against Viktoria Plzen in the Czech Republic on Thursday night. A confusing Cyriel Dessers goal helped cup holders Rangers overcome St Johnstone 2-0 in their last-16 game at Hampden Park. Philippe Clement’s side had plenty of efforts on goal while the visitors struck the woodwork in a goalless first half before the half-time substitute Dessers netted in the 58th minute. It initially appeared as though the referee, Matthew MacDermid, had blown for a foul by Dessers on the St Johnstone defender Jack Sanders at the edge of the box before the forward scored. But after being sent by the VAR to look at it again on his pitchside monitor, MacDermid pointed for a goal, giving the home fans something to cheer at last and angering the visitors. Another Rangers substitute, Ross McCausland, sealed the result in added time. Rangers go into the quarter-final draw but their injury concerns grew. The new signing Robin Pröpper went off before the interval, adding to a list including Nicolas Raskin, Óscar Cortés, Ridvan Yilmaz, Leon Balogun and Scott Wright. There was some positive news in the shape of Brazilian striker Danilo, who featured for the first time since recovering from a knee injury sustained last December. Blair Henderson’s brilliant second-half header was enough to send League Two Spartans into the quarter-finals with a surprising 1-0 victory over Premiership side Ross County at Ainslie Park. Don Cowie’s Staggies arrived at Ainslie Park buoyed by starting the campaign with a six-game unbeaten run in all competitions, but they struggled to impose themselves on their fourth-tier opponents as they suffered a shock last-16 exit from the tournament they won in 2016. Spartans looked the likelier side to score in the first half before prolific striker Henderson got what proved to be the only goal of the game less than a minute after the interval. Aberdeen left it late as a debut goal from Topi Keskinen eventually helped them find a way to overcome Championship side Queen’s Park 1-0 and progress to the quarter-finals. The Dons, who had won all four of their group matches, were the better side against a Spiders team who had lost only once in the competition, to Hibernian. But with Bojan Miovski having departed for Girona in midweek, Aberdeen were not as clinical as they may have been and only Keskinen’s stoppage-time strike separated the sides at Pittodrie. It was no less than they deserved though, as the home side were comfortably in charge for the majority of the game. Dundee stormed into the quarter-finals with an emphatic 6-1 win over 10-man Airdrie at Dens Park. The Dark Blues netted twice before the break through Seb Palmer-Houlden and Jordan McGhee before adding four more goal in the second half from Scott Tiffoney, Antonio Portales, Curtis Main and Lyall Cameron. Adam Frizzell pulled one back for the Diamonds, who had Dylan MacDonald sent off just after the hour.