The Flying Donkeys opened a 10-point gap over the bottom three as 17th-placed Siena failed to respond to Pellissier's effort on the stroke of half-time.
With five games remaining Chievo are unlikely to be sucked back into a scrap to survive but the Tuscans have both Genoa and Palermo snapping at their heels.
Siena approached Sunday's game with a clear determination to take all three points and alleviate the threat of the relegation still hanging over their heads.
That force of will showed in the early exchanges as Angelo sent a deft ball in from the right only for Salvador Agra to miskick when well placed to test Christian Puggioni.
Chievo, though, had their own ideas with a bottom-three finish still a mathematical possibility and they soon bared their teeth as Isaac Cofie fed Pellissier to try his luck.
Innocent Emeghara found himself free in the Chievo area moments later but his first shot flew wide before he headed just over the bar.
Puggioni was then wise to Cofie's shot to the far corner but Chievo would grow in confidence towards the break, eventually squeezing home a deserved opener.
Gianluca Pegolo checked Cyril Thereau's run and watched Boukary Drame's poor conversion sail wide but, deep into stoppage time, Pellissier made the breakthrough.
The veteran striker was on point to sweep the ball over the line as Chievo caught their hosts cold on the counter attack.
Siena were back in the ascendancy as play resumed but there was no explanation as to why Simone Vergassola fired over the bar from close range.
His follow-up cross turned into a shot but Puggioni was not perturbed as it dipped wide of the mark.
The 61st minute brought a moment that could go some way to deciding Siena's future in the top flight.
Paci wheeled away to celebrate after tucking away a Siena corner but he pulled up in disbelief as referee Paolo Valeri disallowed the goal.
The defender was adjudged to have fouled Bostjan Cesar in the build up and Valeri defused persistent protests with yellow cards for Paci and Dario Dainelli.
Still Siena kept coming and, after Emeghara's deflected shot breezed past a post, Puggioni produced a stunning save to keep out a Cesar volley.
The Chievo keeper put his body on the line to keep substitute Michele Paolucci at bay on the stroke of full-time.
Finally, four minutes into time added on, defender Claudio Terzi saw his header miss the mark as the Gialloblu held on to climb three places in the table.