Riordan quickly cancelled out Nick Blackman's early penalty before capitalising on a blunder from Stephen Craigan to hit a 27th-minute winner and justify his recall following suspension.
Hibs then showed the resolve to deprive Motherwell of chances and ensured the win which followed up their 3-0 victory over Rangers in midweek.
Calderwood left out David Wotherspoon from his successful Ibrox line-up to accommodate Riordan, who had been suspended after his red card in the closing stages of Hibs' Edinburgh derby defeat.
Riordan did pay some price for his needless lunge on Rudi Skacel by losing the captain's armband to Ian Murray but he twice linked up with the physical Valdas Trakys to atone for his indiscretion.
There was also a comeback for Dougie McDonald, who was taking charge of his first Clydesdale Bank Premier League encounter since being warned by the Scottish Football Association for lying over the circumstances of his decision to rescind a Celtic penalty at Dundee United last month.
The referee refused to shy away from controversy, appearing to book eight players and handing Motherwell a 10th-minute penalty when Michael Hart felled Jamie Murphy.
Hart put in a risky sliding challenge after the Motherwell winger had got round him on the outside, although the Hibs player claimed he had won the ball. Blackman took his Motherwell tally to nine goals by emphatically converting the spot-kick into the top corner.
Motherwell failed to build on their goal and Hibs were level four minutes later. There appeared to be little danger when Trakys chested the ball into Riordan's path 22 yards out but his first-time effort appeared to wrongfoot Darren Randolph before nestling in the bottom corner.
The goal lifted the hosts and Riordan was presented with an easier chance but shot well over from 12 yards after Randolph had blocked Edwin de Graaf's flick following an excellent cross from Jonathan Grounds.
But Riordan grabbed his second after Craigan's error allowed the former Celtic player to slot home from 12 yards.
Motherwell had gone missing as an attacking force following their opener but they sprung into action after switching to a back three.
Alan Gow headed Chris Humphrey's cross back across the face of goal and both Humphrey and Murphy came close. But Motherwell could not sustain their pressure for the rest of the half and they struggled to break Hibs down after the break.
Riordan had two half-chances to complete his hat-trick before the hour mark, curling a free-kick just over and then rounding Randolph only to see Mark Reynolds sweep up. The game was held up for more than five minutes after Gow caught Francis Dickoh late with an aerial challenge. The Hibernian defender was carried off on a stretcher with Paul Hanlon coming on and Gow continuing after treatment.
Steven Saunders had the ball in the net in the 71st minute but he was immediately flagged offside following Steve Jennings' through-ball.
The officials found themselves at the heart of controversy when McDonald let go a clear handball from John Rankin deep inside his own half before Riordan was dubiously flagged offside from the midfielder's subsequent pass. McDonald appeared to flash his yellow card at Saunders, Humphrey and Jennings as the Motherwell players protested.
The visitors pushed forward but they were frustrated by a solid Hibs unit, which now had Steven Thicot on for the booked Liam Miller alongside Murray in central midfield.
Riordan came closer to his hat-trick in the 88th minute with a brilliant turn and volley, matched by Randolph's fingertip save and Grounds soon curled just wide.
Hibs remained firm and the game almost boiled over during seven minutes of injury time.
Murray and Craigan were booked after the Hibs captain's poor challenge on Randolph sparked a scuffle and Reynolds and Trakys were also cautioned after the Motherwell defender reacted angrily to a late challenge.