The Scotland forward struck a sweet volley in the first half - with the aid of a deflection off Bairns centre-half Brian McLean - before settling the outcome two minutes from time at Easter Road.
The victory saw Hibs capitalise on Rangers' loss at Aberdeen to go joint second and sit just two points behind leaders Celtic in the race for the title.
But while John Hughes' side stretched their unbeaten league run to nine matches, his charges were forced to scrap for the success against his former team. The bottom-placed Bairns again showed signs of promise and had their chances, as well as having a 'goal' chalked off shortly before Riordan struck the opener.
Hughes made three changes, one enforced, as Kevin McBride's ankle knock kept him out and John Rankin deputised. Lewis Stevenson and Abdessalam Benjelloun also dropped to the bench for Merouane Zemmama and Colin Nish.
Falkirk were unchanged after new French signing Toufik Zerara failed to gain international clearance in time. Eddie May's outfit threatened first but Chris Mitchell, a goal hero last weekend, was unable to repeat his accuracy as his second-minute free-kick whistled over.
Hibs replied with a superb long ball from Riordan towards David Wotherspoon but the teenager was stretching as he clipped past the back post.
The Bairns were looking confident, clearly buoyed by their recent results, yet the hosts had another sight of goal on 13 minutes only for Nish to head over Riordan's cross.
Darren Barr then gave the ball away in the centre circle allowing Hibs to break and only desperate challenges twice blocked out Riordan.
A further opportunity quickly came after Nish and Zemmama played a neat one-two on the edge of the penalty area, with the latter denied by Robert Olejnik.
Vitor Lima replied with a low shot pulled just wide, before Hibs should have broken the deadlock on 25 minutes.
Ian Murray's cross from the left found Nish in space just eight yards from goal, but Mitchell blocked his shot superbly to deflect just wide.
Pedro Moutinho tested Graham Stack with a low drive at his near post, before May took off Danijel Marceta, presumably tactically, for fit-again Alex MacDonald.
Falkirk soon went closer as Mitchell's corner saw Carl Finnigan bullet a header towards goal only for Wotherspoon to brilliantly clear off the line. The Bairns immediately cut the ball back for Ryan Flynn to net, but the assistant referee had ruled that Wotherspoon's initial clearance had gone out for another corner.
Falkirk were quickly made to rue their ill luck as Hibs made the breakthrough on 33 minutes.
Zemmama's chip to the back post picked out Riordan who showed excellent technique to drill a left-foot volley across Olejnik - with the ball helped in by McLean.
Nish was denied a second as Olejnik somehow clawed his header off the line. Barr then saw a header drop just wide as Hibs failed to deal with a set-piece near half-time.
Hughes made an unexpected change at the break with Stack replaced by Yves Ma-Kalambay.
The hosts were soon back on the front foot with Riordan's cross from the left falling into the path of Liam Miller, whose 18-yard drive was only deflected wide thanks to last-ditch defending.
An audacious chip from Moutinho in the 57th minute almost saw Falkirk draw level but Ma-Kalambay back-tracked to impressively tip his effort onto the bar and wide.
Anthony Stokes, who had been quiet, then played in Nish but as Olejnik saved well the offside flag was raised against the striker.
The game became scrappy due to a host of substitutes, but Mitchell wasted another free-kick opportunity as the visitors pressed for the leveller.
As Hibs became nervy, especially in defence, Falkirk sensed their chance and Ma-Kalambay was fortunate to only just block out sub Lee Bullen following a long ball.
But Riordan eased the home tension on 88 minutes with a sweeping left-foot finish at the back post after a fine ball across from Wotherspoon.