Riordan was confronted by several Hearts fans as he celebrated his 79th-minute spot-kick moments after Christos Karipidis had been sent off for a professional foul.
Hearts struggled to create chances apart from a brief flurry midway through the second half as they missed a chance to consolidate third position in the Clydesdale Bank Premier League.
The drama came towards the end of a match previously lacking excitement, although Hibs manager Mixu Paatelainen would have been delighted by his young side's display amid a selection crisis.
Chris Hogg became the fourth Hibernian player to miss the game through suspension after the club's appeal against his red card in Saturday's late defeat by Dundee United.
With Rob Jones and Sol Bamba also on that list, along with striker Colin Nish, Ian Murray and Steven Thicot formed a makeshift but effective partnership in central defence.
Jonatan Johansson and Denes Rosa also dropped out through injury with Alan O'Brien, Paul Hanlon and Ross Chisholm stepping in.
Hearts pushed Hibs back in the early stages but a half-chance for Calum Elliot was all they had to show for their possession.
Elliot, who signed a new three-year contract earlier in the day, had a first-time shot on the turn saved at the second attempt by Yves Ma-Kalambay after Murray had Lee halted Wallace's driving run into the box.
Riordan's policy of playing right on the home side's advanced back line almost paid off midway through the half when he peeled off to collect O'Brien's pass as Hibs broke quickly.
The forward fired a 20-yard strike between two Hearts players and Marian Kello had to get down well to push the ball wide.
Hibs grew in stature and clever through-balls by the impressive Chisholm almost sent Fletcher and Riordan away.
The home fans were growing frustrated and Csaba Laszlo made a tactical substitution in the 33rd minute, with striker Christian Nade replacing Eggert Jonsson.
Jonsson, making a rare appearance in his preferred central midfield position after a season spent covering elsewhere, made a gesture of bemusement towards his manager before walking down the tunnel.
Hibs continued to edge play and John Rankin hooked the ball wide from a difficult angle after running on to O'Brien's dink over the top.
Hearts improved marginally in the closing stages and Elliot saw a long-range drive comfortably saved.
Some decent Hearts possession came to nothing early in the second half and Riordan's clever touch created space for O'Brien to shoot at the other end, however the winger was off target from 20 yards.
Hearts soon created a better chance when Elliot played David Obua in at the byline but David van Zanten produced a brilliant clearance to stop Nade converting at the far post.
The home side stepped up a gear and Andrew Driver - having a quiet game amid reports Coventry are considering a bid for his services, with manager Chris Coleman at the match - saw his controlled volley turned wide by Ma-Kalambay following Bruno Aguiar's deep cross.
Hearts continued to press and Elliot failed to turn Wallace's low cross inside the near post under intense pressure from Thicot, before Obua volleyed well over from 16 yards.
However, the game turned following a simple long ball.
Riordan ran on to Ma-Kalambay's long ball before being brought down by Karipidis, who was sent-off by Steve Conroy.
Riordan sent Kello the wrong way and then chose to run away from his own fans and celebrate in front of the home support in the Wheatfield Stand.
Around half a dozen supporters ran on to the pitch to confront the Hibs players and one almost got to Riordan before being dragged away by stewards.
Hearts threw the ball forward in the closing stages but a harmless overhead kick by Nade was the best they could muster.