Riordan struck twice after the break - his second a stunning free-kick - after Falkirk had dominated the first half of this Scottish Premier League game.
On-loan Liverpool winger Ryan Flynn put them ahead but the outstanding Sol Bamba levelled against the run of play shortly before half-time.
Anthony Stokes was handed his Hibs debut against the club for whom he scored 14 goals in 16 SPL starts while on loan three years ago.
The striker, who signed from Sunderland yesterday for an undisclosed fee, replaced David Wotherspoon, whose debut goal against St Mirren last week was not enough to keep him in the side.
Hibs also drafted in David van Zanten for the fatigued Kevin McCann, while Falkirk replaced the injured Vitor Lima with Alex MacDonald.
Today's game was Hughes' first return to Falkirk since quitting to take charge of Hibs this summer.
The home side could have taken an early lead when Carl Finnigan was presented with the ball 10 yards out but he could not control it and Bamba cleared.
Scott Arfield - who has been linked with a move away from Falkirk - then fired narrowly wide from 25 yards.
Kevin McBride had been booed from the first whistle by his former fans and got another earful, and word from referee Steve Conroy, after a late tackle on Burton O'Brien.
Falkirk were unlucky not go ahead when a backpedalling Finnigan nodded Darren Barr's right-wing ball against the crossbar.
Stokes had been subdued but finally threatened with a cute turn and left-foot shot saved easily by Robert Olejnik.
Otherwise, Hibs were second best as Falkirk pressed well, Finnigan leaving Chris Hogg in a heap in the box before curling a shot too close to Yves Ma-Kalambay.
And the home side took a deserved lead in the 25th minute when Flynn's right-foot finish from the corner of the box found its way through a crowd of players and past Ma-Kalambay.
There were then three bookings in quick succession, Van Zanten for a crude challenge on Flynn, Hogg for a tackle on Finnigan, and Thomas Scobbie for foolishly kicking the ball into the stand occupied by the away supporters.
Stokes had a chance to level when he lifted Paul Hanlon's super through-ball over Olejnik but also over the bar.
Arfield's free-kick then caused sheer panic in the Hibs defence but Bamba came to the rescue again.
And he was the hero at the other end five minutes before half-time, charging onto John Rankin's wicked corner to power home a header.
Bamba was booked for his celebration and Rankin followed suit shortly after the restart for a tackle that briefly forced Marc Twaddle from the field.
Finnigan was next to see yellow after a touchline altercation with Bamba.
The pair clashed again on the halfway line, Finnigan making the most of a tackle from behind.
Stokes should have put Hibs ahead when Colin Nish's hooked ball sent him clear but his tame lobbed finish failed to find the net.
It did not matter as the visitors won a 57th-minute free-kick, which was fizzed in from the right wing by Rankin and turned in at the near post by Riordan.
McBride was carded after felling O'Brien before Falkirk threw on Danijel Marceta for MacDonald.
The substitute was soon fouled by Patrick Cregg, who became the sixth Hibs player to see yellow.
Hanlon had to be on hand to clear a dangerous cross from in front of his own goal.
Hogg's attempted clearance then only found Arfield, who juggled the ball before volleying at Ma-Kalambay.
Hibs brought on Wotherspoon for Cregg and sealed the victory 10 minutes from time when Riordan stepped up to curl a stunning free-kick past Olejnik.
The match-winner was brought off for Abdessalam Benjelloun, while Falkirk replaced McNamara for Dayne Robertson.
Benjelloun and Marceta both went close late on at either end but the outcome was already assured.