Goals from Morgan Neill, Rory McAllister and Leighton McIntosh gave Ex-Bairns boss Paul Hartley all three points.
Martin Rennie was announced as the club’s new head coach on Friday night after the departure of Paul Sheerin, however the 46-year-old watched on from the stand with coach Danny Grainger taking the side.
The first chance of the match fell to the Bairns five minutes in. Aidan Keena found the onrushing Callumn Morrison with a defence splitting pass, but the winger fired an effort just wide.
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Seb Ross was next to go close with a low drive that was eventually held by Stuart McKenzie.
Falkirk dominated the opening stages as Keena’s deflected effort somehow went the wrong side of the far post.
On 22 minutes defender Neill unleashed a thunderbolt from range to put the visitors ahead, Paddy Martin was left hopeless as the ball crashed into the top corner.
There was no love lost between the sides and there were a flurry of bookings as referee Calum Scott struggled to control proceedings.
Keena went close again when found in the box by Ryan Williamson but a last-ditch tackle from Harry Milne prevented a certain equaliser.
Cove doubled their lead on 41 minutes after McAllister escaped the attentions of the Bairns backline to score on the half volley in the box.
Paul Hartley’s side should have sealed the three points moments into the second half when Martin’s indecision gave Fraser Fyvie the chance to pass to McAllister who fired over the bar.
Samuel Ompreon came on for a rare appearance with Seb Ross going off on 57 minutes as Falkirk looked to get a goal back.
Martin made two superb saves on 70 minutes to keep the score at two after a diving save to deny a volley in the box and a rebounded header at the near post.
The Bairns nearly got back into the match in spectacular fashion with Keena testing the goalkeeper from 30 yards with McKenzie lucky to have kept the ball out of the net.
Falkirk huffed and puffed but failed to create any meaningful chances with Cove sealing the result from substitute Leighton McIntosh’s delightful chip on the counter attack on 90 minutes.
Ex-Aberdeen defender Shay Logan was sent off at full time for a second yellow card.