Riordan's 63rd-minute strike at Easter Road on Wednesday night was Hibs' first goal since the 2-2 draw with Dundee United on December 29 and Wotherspoon added a second in stoppage time to end a 12-match winless run.
The result handed manager Colin Calderwood a record of three wins and 12 losses from 18 matches in charge.
St Mirren, who began the evening two points and a place above Hibs in the SPL table, fell to 11th in the table after struggling to test Hibs' vulnerable defence.
The Buddies are now four points above bottom club Hamilton having played a game more. Accies have two games in hand on Hibs.
Hibs required a first win since the November 13 defeat of Motherwell and a first goal of 2011 to climb above their opponents into 10th place and they began on the attack.
Akpo Sodje, who made his debut after signing from Charlton on deadline day, was recruited to take the full burden away from top scorer Riordan as Calderwood's backing by the Easter Road board was demonstrated by the signings of six players in the January transfer window.
Four were in the starting line-up tonight and Matt Thornhill, signed from Nottingham Forest last week, shot wide from the edge of the area after four minutes.
A poor backpass by Callum Booth and a weak defensive header by Francis Dickoh exposed the hosts' defensive frailties soon after but Steven Thomson's corner came to nothing for Saints.
Richie Towell dragged a shot across goal, Sodje fired wide and Thornhill shot off target as Hibs continued to dominate the early possession.
Towell's deflected drive was saved by Paul Gallacher, but Thornhill sliced the rebound from a narrow angle with the goal gaping.
Sodje shot wide on the turn after receiving Ian Murray's cross before Thomson shot off target from 30 yards with the goal vacant after Graham Stack - the latest stopper to be used in Calderwood's goalkeeping rotation policy - raced off his line to clear a through ball with a header.
After Saints had been forced into an early change with Hugh Murray replacing Paddy Cregg, Michael Higdon saw the visitors' first effort on target saved by Stack low to his left.
Booth raced down the left for Wotherspoon to head wide as Hibs finished the half on the attack but still chasing a first goal of the calendar year.
Thomson had an effort blocked by Ian Murray within a minute of the restart before Victor Palsson tackled Higdon on the edge of the visitors' area and then found Sodje.
However, the striker snapped at his effort and could not find the target.
Thornhill, Ian Murray and Palsson were booked in quick succession for Hibs in a sign of their growing frustration as the Buddies remained resistant to their hosts' attacking threat.
But a goal finally came after 63 minutes, ending Hibs' barren run of more than 11 hours.
Ian Murray won a header 30 yards out after Saints half-cleared Stack's long clearance and Sodje knocked down for Riordan to skilfully net low beyond Gallacher. It was his ninth of the season.
Ian Murray then hit the outside of the post with a header from Riordan's cross after 76 minutes as Hibs went close to a second.
Gallacher denied Riordan after the forward had made space for a shot, with Saints increasingly stretched as they looked to get forward.
Riordan was then sacrificed for Danny Galbraith to a rousing ovation from the home fans before Wotherspoon swept in a second from close range as Hibs recorded just a fifth win of the season.