The Gers took the lead in 10 minutes with Jukka Santala opening the scoring.
Two minutes later impressive Rwandan winger Oscar Hatungimana equalised for the Dutch visitors. He unleashed a powerful shot from outside the box which hit the bar - he ran in and collected his own rebound and fired it past Callum Reidford.
Goals from Tom Brighton and Bajram Fetai quickly put the Gers back in the driving seat.
In 32 minutes Fetai scored again - a simple tap-in from a cross supplied by Derek Carcary. Two minutes later Andy Dick got the fifth for the Gers - Fetai this time threw in a cross which Carcary headed down for Dick to finish off.
A host of second half substitutions turned the contest into a more even affair in the second half.
Groningen pull back another after Jordan McMillan panicked in the 63 minute under pressure from Hatungimana and his clearance ended up in his own net.
Carcary was particularly impressive coming back from a groin injury. He was very confident on the ball, prepared to take on several men on his own and fire in shots. Defender Brian Gilmour proved himself cool under pressure as he played the ball out of his own box.