Xherdan Shaqiri had given the Potters the lead just before the half-time whistle, only for Butland to fumble the ball into his own net with 20 minutes remaining.
However, the England goalkeeper redeemed himself with a number of important interventions to earn his side another point in their battle to avoid relegation to the Championship.
Stoke are now a point from safety, while Leicester move into seventh place in the top-flight standings, despite extending their recent league record to just two wins from 11 matches.
In the build-up to this game, Claude Puel had spoken about his team squandering points in their most recent league matches, but his side dominated the opening stages with Matty James firing an early effort marginally over the crossbar.
Riyad Mahrez was a constant threat for the home side but was unable to test Butland in the Stoke goal while up the other end, January signing Badou Ndiaye had a 25-yard strike well saved by Kasper Schmeichel.
As the first half progressed, Mahrez continued to threaten an opening goal but Leicester were struggling to put the visitors under any sustained pressure and they were eventually made to pay just before the break.
A mistake from Wilfred Ndidi in the middle of the pitch resulted in the ball finding its way to Shaqiri, who advanced towards goal before curling a 25-yard shot into the net via the inside of Schmeichel's left-hand post.
After the restart, Leicester went onto the front foot but despite forcing Stoke back into their own defensive third, the Foxes were still unable to create any clear-cut opportunities.
Stoke were prepared to play a waiting game rather than searching for a second goal, but the visitors almost doubled their advantage when Schmeichel's clearance went straight to Shaqiri who was waiting 40 yards out, only for the Swiss to curl his resulting shot just wide of the target with the goalkeeper scampering back across goal.
Paul Lambert felt that his side were in control of proceedings and took the opportunity to introduce teenage forward Tyrese Campbell for his debut, but the final quarter of the game belonged to their hosts.
With 20 minutes remaining, Leicester were gifted an equaliser by Butland, who fumbled the ball into his own goal after trying to anticipate that Jamie Vardy would get a touch on Marc Albrighton's cross from the right.
Leicester soon set about trying to find a winner, but Butland redeemed himself with a stunning one-handed save to deny Mahrez from distance, before Harry Maguire clattered the post with a close-range effort moments later.
Stoke continued to push for a second goal of their own, but they were living dangerously at the back and Charlie Adam's poor header back towards Butland only found Mahrez, who was denied by a combination of the Stoke goalkeeper and Kurt Zouma.
From the resulting set piece, the ball was played to Mahrez who found Maguire with an outswinging cross, only for the defender to head against the far post before the away team eventually cleared.
Stoke finally won their first corner of the match in the fourth minute of added-on time but nothing came from Shaqiri's delivery and both teams were forced to settle for a point apiece.
LEICESTER CITY (4-4-1-1): Schmeichel; Simpson (Iheanacho 62'), Morgan, Maguire, Chilwell; Albrighton, James, Ndidi, Gray (Diabate 61'); Mahrez; Vardy
STOKE CITY XI (4-3-3): Butland; Bauer, Zouma, Martins Indi (Adam 74'), Stafylidis; Cameron, Allen, Ndiaye; Choupo-Moting (Johnson 84'), Shaqiri, Diouf (Campbell 64')