Paul Hartley watched his side ease last year’s beaten Scottish Cup finalists out of the tournament in last night’s long-awaited fourth round tie then suggested that his team have the firepower to have a chance of going all the way this time around.

Reminded that he had said ahead of this season that his target was to steer the club to a first major trophy in more than 40 years, the Dundee manager - who reportedly snubbed BBC television last night in refusing to give them an interview following his recent spat with pundit Pat Nevin - did not shy away from having also predicted that they were capable of it.

“I believe that,” he said.

“I think it’s just getting through the games in the cup, whether it’s good performances or scraping a win. We’ll take any win.

“If we can keep progressing then great. We would love to do something in terms of a bit of silverware or getting close to it. Every game we know where we’re at and we have to have a high level of performance, but we’ve shown that with (Gary) Harkins, (Greg) Stewart, (Rory Loy and (Kane) Hemmings we’ve got guys who can score goals for us and cause problems.”

On a night for the superstitious at Dens Park it was third time lucky for Dundee in terms of getting this match on, let alone winning it, while Falkirk’s fine unbeaten run ended at the 13 mark.

With the night’s shock result happening across the county of Angus, where a Kevin Kelbie goal saw non-league Linlithgow Rose knock Forfar Athletic out of the tournament at Station Park, the Premiership team was made to work as hard to get through as had been widely expected.

Peter Houston, Falkirk’s manager, understandably reckoned his had even been the better team through that period, but the quality of Hemmings at the business end of the pitch ultimately made the difference.

Playing into the strong wind and towards the half of Dens Park that did not require to be patched up after the water-logging issues that had twice caused the postponement of this tie, Falkirk set out looking like a team buoyed by the confidence of that unbeaten run.

Aaron Muirhead knocked a volley just wide from an early Craig Sibbald corner after performing a spot of acrobatics to get his foot to the ball and midway through the half Sibbald cut in from the right touchline to tee up Will Vaulks just outside the box, his powerful strike forcing Scott Bain to dive sharply to his left to turn it away and the goal-keeper had to look lively going the other way as a Muirhead cross-shot from the right swerved dangerously goalwards.

Having the wind at their backs was meanwhile causing the home team as much trouble as anything else as they repeatedly overhit attempted through balls, albeit Kane Hemmings was also culpable, misjudging a string of runs in keeping the linesman busy.

He was rewarded for living dangerously, though, when it again looked marginal as a Paul McGowan pass put him in behind the Falkirk defence wide on the right. With defenders scurrying back Hemmings’ well struck right-footed shot from outside the penalty box on the right was deflected high into the air and over a hapless Danny Rogers.

Registered in 39 minutes the lead lasted just two more and this time McGowan was at least partly culpable as he was dispossessed too easily midway inside his own half in trying to set up a counter-attack.

The hobbling Kostadin Gadzhalov played John Baird onside as the ball was knocked into the danger area, allowing him to gather then home in on goal attempt and while his attempt was half-blocked, the ball broke across goal where, from close range, Paul Watson forced it home.

Turning into the breeze Dundee gradually began to impose themselves and their in-form striker then broke the deadlock a second time, Paul McGinn finding space in the penalty area on the right, spotting two navy blue jerseys at the far post and chipping it invitingly across Rogers towards them, Hemmings almost inevitably reacting first to volley it home left-footed.

That came on the hour and 13 minutes later he provided an assist on the goal that wrapped things up as he collected the ball wide on the right, spotted Gary Harkins drifting into space in the middle of the park and picked him out early enough to let his captain take a touch, steady himself and then, from the edge of the box, slide the ball beyond Rogers and inside the goal-keeper’s right post.

Greg Stewart hit the post soon after, but had he scored it would have cast a rather unfair reflection on the evening’s events.