Already relegated, the part-timers were shown no mercy by Paul Hartley’s side.
Aaron Muirhead cooly rounded City goalkeeper Graeme Smith to break the deadlock in the 17th minute.
The Angus club could not cope with Falkirk’s pace and trickery, the second arriving in the 29th minute when Craig Sibbald slotted in Louis Longridge’s cut-back.
City then imploded in having two men shown straight red cards within the space of three minutes.
Sean Crighton’s challenge on the irrepressible Alex Jakubiak was high and reckless in the 40th minute. He was followed down the tunnel by Paul McLean, who tripped the same player.
Andrew Nelson added a third on the hour mark.
“We got the job done,” said Bairns manager Paul Hartley. “I felt we were excellent in the first half and it was a strange game in the second because of what we faced with all the possession.”