Falkirk remain unbeaten in eight games at the start of this campaign and now have a six-point lead at the top of League One.
The first incident of note came with just two minutes on the clock when Clyde players screamed for handball and a penalty after Hall connected with a David Goodwillie cross. But referee Colin Steven was unmoved.
A dangerous cross from the left flashed into the Clyde box on 12 minutes but Falkirk's Anton Dowds couldn't make meaningful contact in the centre.
An Aidan Connolly centre then found the visitors’ Calumn Morrison who headed weakly at home keeper Matej Vajs.
After a fairly uneventful first half hour, the game came alive when Telfer gathered the ball on the edge of the box and sent a brilliant 20-yard shot flying past Vajs.
Clyde were frustrated on 35 minutes when Goodwillie brilliantly bulleted in a header following a cross from the right but the goal was disallowed for offside.
A fine run forward by Connolly culminated in a powerful left footer from long range going a foot over the bar.
Telfer was booked for pulling back Cunningham before an outswinging Cunningham corner was headed over by Goodwillie in the final action of the first half.
Falkirk's Dowds was booked for a late tackle on Jamie Bain early in the second half.
Dowds had a shot blocked before play surged to the other end where Clyde forward Kristoffer Syvertsen was booked for diving after going down in the box following a Goodwillie pass.
The Bairns doubled their lead on 55 minutes when Mercer headed in a wickedly delivered Connolly corner from the right.
Dowds then had a shot blocked by Tom Lang, before it was 3-0 when Hall stabbed the ball in after another Connolly corner had caused chaos in the home box.
Clyde defender Lang then wasted a glorious chance at the other end when his left footed effort from close range was well saved by Mutch.
The Bully Wee should have pulled one back on 75 minutes when Syvertsen's fine run put Cunningham clean through on Mutch but the keeper saved well.
Clyde nearly scored a late consolation when sub Josh Jack shot just wide of the far post from 20 yards with his left foot. Jack then sent another effort wildly over.
On a good day for Falkirk, rivals Cove Rangers lost 1-0 at Dumbarton.
The Bairns, who have won six and drawn two of their opening eight league games, now have a six-point lead at the top over Partick Thistle.
Falkirk are next in league action at home to Airdrieonians next Saturday.
On this form, the Bairns look a good bet to land the League One title this campaign.
Falkirk: Mutch, Mercer, Dixon, Hall, Dowds (Deveney 87), Connolly (Todd 76), Gomis, Sammon (Francis 65), Telfer (Miller 76), Kelly, Morrison (Leitch 65).
Referee: Colin Steven