The Deesiders handed the Highlanders their worst ever defeat since joining the Junior ranks in an impressive display at a sun baked Crombie Park. City had no answer to the onslaught and failed to muster a single shot on target.
City were the first to attack but Andy Fraser could only balloon over from a decent Gary Miller cross.
With only two minutes on the clock a long Hugh Robertson ball was taken down by Jamie McAllister who blasted the ball past the vertically challenged Iain Young in the City goal.
Jamie McAllister added his second almost straight from the kick off when he finished clinically following a typical mazy run from Dod McBain. It was all one way traffic with Mike Taylor heading over from a McBain deep cross.
The third was not long in coming and this time Scott McArthur jinked forward before despatching a terrific left foot curler into the net from the edge of the area.
City were looking totally bemused already and it was no surprise when Ian Leith made it 4-0 just a minute later with a fine finish.
Not surprisingly Culter took the foot off the pedal but City still could not muster a decent attack before McBain and Taylor both went close.
The fifth came in the 22nd minute following a flowing move involving Allan Youngson and McAllister and Mike Taylor was on hand to net from close range.
It could have been six, or more, before half time with Youngson going close on two occasions and Leith came even closer with a cute lob which drifted just over.
The home side sent on Ross McWilliam, Robbie Brown and Andy Sim for McAllister, Colin Craik and McArthur at the start of the second period but it was still one way traffic.
Ross McWilliam, from a suspiciously offside position, netted with almost his first touch of the ball when he walked the ball home following a deep Leith header. Ross McWilliam then doubled his tally with a fine solo effort created by Taylor. It was exhibition stuff now with Culter stroking the ball about without creating very much.
The scoring was complete with 33 minutes still to play when Dod McBain thundered an absolute beauty high into the net from long range.
City by this time were totally frustrated and looked completely demoralised and this showed when referee Graeme Jack flashed a couple of yellow cards to the Highlanders.
Culter: Duguid, McArthur, Robertson, Reid, Wilson, Craik, Youngson, McBain, J. McAllister, Taylor, Leith. Subs: McWilliam, Sim, Brown, Rattray, Farquhar.
Inverness: Young, MacLeod, Thomson, MacDonald, Smith, Fuller, Munro, M. MacKenzie, K. MacKenzie, Fraser, Miller. Subs: Curran, Mulligan, Khomoro, Reid.