Giorgi Nemsadze squandered a great chance for Dundee as they fought out a goalless first half with Hearts at Dens Park.
Nemsadze sidefooted over in the 36th minute after Caniggia had driven in a low cross from the by-line.
Hearts managed to respond a minute later and Roccati nearly got a wake-up call when Flogel attempted an audacious overhead kick from Austin McCann's cross.
Both teams were in buoyant mood before kick-off after their midweek victories.
Hearts had beaten Kilmarnock and Dundee were fresh from an unexpected win at Rangers.
The extra incentive for Dundee was to seek revenge for their exit at the hands of Craig Levein's team in the Scottish Cup.
The opening period was entertaining, with Hearts spurning a good chance to go in front in the ninth minute.
Striker Andy Kirk managed to dispossess Barry Smith 25 yards out but the Northern Ireland international could only drill his shot inches wide when clean through on goal.
Dundee managed to assert themselves after this early scare, and nearly went in front themselves after 14 minutes.
Initially it was their influential midfielder Giorgi Nemsadze who assisted Claudio Caniggia to put Juan Sara into space, only for the Argentinian hitman to blast against Hearts keeper Antti Niemi.
Hearts midfielder Colin Cameron, back in the side having recovered from injury, decided to involve himself in proceedings midway through the half.
When the Scotland man was set up by Juanjo, he tried his luck with a well-placed shot from 20 yards, but Marco Roccati did well to deny him.
Cameron tried again in the 27th minute from the same position, but his speculative shot was well over.
Dundee looked casual at the back, and when Smith's clearance ricocheted off Kirk, the ball fell nicely to Thomas Flogel, and amid suspicions of offside Roccati reacted best by tackling the Austrian just outside the penalty area.