First-half goals from Cameron Stewart and Johnnie Jackson had looked to hand the Addicks their third away win of the season, but a Michael Morrison own goal and an Ishmael Miller penalty earned the hosts an unlikely point.
It might have been even better for Yeovil as Charlton were left to play out the final 12 minutes with a man less following Jackson's sending-off, but they could not find a winner.
The sides came into the game as the league's joint lowest scorers with 14 goals each, and the game threatened to descend into a drab stalemate after a quiet opening half-hour.
Yeovil manager Gary Johnson named an unchanged side as he searched for a third successive win, and the Glovers started the match in the ascendancy.
Midfield talisman Ed Upson came close to notching a memorable opener when his dipping 25- yard volley soared narrowly over Ben Alnwick's crossbar.
But the Addicks, who had lost four of their last five and were without a goal in 380 minutes of football, began to dictate play as the half progressed with returning skipper Jackson at the heart of his side's attacking play.
Winger Stewart also enjoyed a dazzling first half at Huish Park, and the Glovers were warned of the Hull City youngster's prowess shortly after the half-hour mark as he cut inside from the left flank and saw his stinging drive brilliantly saved by Yeovil goalkeeper Chris Dunn.
However Stewart, who spent two months at Yeovil under Terry Skiverton in 2010, made the home side pay for some slack defending moments later. Picking the ball up midway in the Glovers' half, he skipped past two defenders before rifling a low shot into the bottom corner from 20 yards.
Yeovil's misery was compounded just before the break when Stewart evaded defender Luke Ayling, before producing a pinpoint cross to the back post to Jackson, who nodded home from close range.
Johnson made a double substitution at half-time to galvanise his side, but Chris Powell's outfit continued to impress with midfielder Jordan Cousins seeing his shot fizz wide.
An injury to Liam Davis early in the second period did little to aid the Glovers cause, and they had goalkeeper Dunn to thank on the hour-mark after he produced another stunning save to keep out Simon Church's overhead kick.
The Glovers hit back with 18 minutes remaining after Joel Grant's cross fortuitously cannoned off defender Morrison and into the net.
Four minutes later on-loan striker Miller drew his side level after coolly converting from the spot after Grant was tripped by Andy Hughes.
The Addicks' torrid second half worsened moments later when Jackson was given a straight red card for a late tackle - but the visitors held on to earn a point.