Hibernian reached the Scottish Cup semi-finals after a day to forget for Falkirk goalkeeper Allan Ferguson.
Riordan shot Hibs into an early lead
The visitors were gifted an early lead when Ferguson made a mess of Derek Riordan's long-range free-kick.
Ferguson was at fault again when he spilled a Riordan shot and Garry O'Connor slammed in the loose ball.
Daniel McBreen hit back for Falkirk but Ivan Sproule prodded in shot, Gary Caldwell added a strong header and Steven Fletcher shot home late on.
The scoreline rather flatters Hibs, who have not won the trophy since 1902, because Falkirk enjoyed long spells of pressure.
However, the home side lacked a cutting edge in front of goal, while they contributed heavily to their own downfall with some glaring mistakes.
High winds were making life difficult, with the sides relying on long balls because of the badly rutted playing surface.
Hibs made the breakthrough after nine minutes thanks to a blunder from Bairns goalkeeper Ferguson.
Riordan tried his luck with a free-kick from 30 yards and Ferguson spilled the ball through his own legs as it bounced just in front of him.
Patrick Cregg shot wide from distance and Jack Ross saw a drive whizz over the crossbar as Falkirk searched for an immediate response.
A Cregg free-kick from 20 yards was also just too high to trouble visiting goalkeeper Simon Brown.
Hibs were given a scare three minutes before the half-time break when Brown failed to gather a corner kick and Kenny Milne crashed a header off the crossbar.
Caldwell was on target against Falkirk
Hibs winger Sproule had been having a quiet game but was unlucky to see his low shot flash wide of the post after a neat passing move.
Hibs then doubled their advantage and it was down to another mistake from Ferguson.
Riordan curled in an ambitious effort that Ferguson could only awkwardly parry into the path of O'Connor, who blazed the ball home from six yards.
Falkirk hit back straight away, with substitute Russell Latapy splitting the Hibs defence and McBreen running on to the pass and drilling a shot beyond Brown.
The Bairns fightback was short-lived, however, as Hibs regained their two-goal cushion when Milne slipped up while attempting to deal with a Fletcher delivery and Sproule nipped in to stab the ball into the net.
The Hibs lead was stretched yet further when Caldwell rose high in a crowded penalty box to head home a Stephen Glass corner kick.
McBreen missed a golden chance for a second goal, while the jittery Ferguson let an O'Connor shot squirm through his grasp and Andy Lawrie cleared off the line.
There was to be more misery for the home side when Fletcher hit the back of the net late on, with the aid of a slight deflection.
Falkirk: Ferguson, Ross, Twaddle (Lima 80), Milne, Lawrie, Cregg, Craig (Latapy 68), Thomson, Moutinho, Gow, McBreen. Subs Not Used: Howard, Scally, Rodrigues.
Booked: Cregg. Goals: McBreen 70.
Hibernian: Simon Brown, Whittaker, Murphy, Caldwell (Konde 79), Smith, Stewart, Thomson, Glass, Sproule (McCluskey 79), Riordan (Fletcher 72), O'Connor. Subs Not Used: Malkowski, Hogg.
Booked: Riordan. Goals: Riordan 9, O'Connor 67, Sproule 74, Caldwell 77, Fletcher 88.
Ref: K Clark