Substitute Wallace curled in a fine 96th-minute set-piece from the edge of the penalty area that gave Kasper Schmeichel no chance and ensured that Sean Dyche's men secured their fourth draw of the Premier League season.
With one minute of the seven added minutes to go, Leicester looked on the verge of victory thanks to Riyad Mahrez, who created one and scored the other.
The Algeria international forward shone on his return to the starting line-up and set up Jeffrey Schlupp's opener before edging the home side back in front after Michael Kightly had ended Burnley's goal drought to level.
However, Wallace had the final say as his exquisite effort earned a share of the spoils.
The point extends Leicester's unbeaten home start in the league to four games, while Burnley climb off the foot of the table at the expense of QPR.
Both sides made two changes following defeats last weekend with Schlupp and Mahrez both drafted into the Leicester starting XI, while Ashley Barnes and Stephen Ward came in for Burnley.
A spritely start from the visitors failed to produce a clear goal-scoring opportunity and Mahrez sparked Leicester into life with an 18th-minute effort that began inside his own half.
Having escaped the attention of three defenders, Mahrez raced towards the Burnley box before unleashing a low shot that goalkeeper Tom Heaton pushed away.
Leicester's pressure eventually told after 33 minutes to kick-start a frantic seven-minute period.
Mahrez was given time to deliver a low cross from the right that found Schlupp in the penalty area and the 21-year-old made no mistake with a first-time finish past Heaton.
Burnley, though, were not behind for long as they finally broke their 565-minute goal drought courtesy of Kightly, the winger getting on the end of a Lukas Jutkiewicz knockdown to bundle past Schmeichel from close range.
However, Burnley's joy was short-lived as Leicester went straight down the other end to re-take the lead.
Jamie Vardy found room on the left of Burnley's penalty area and his cross was deflected off Jason Shackell's heel to the back post where the unmarked Mahrez headed home.
Jutkiewicz had the best chance at the start of the second half as the striker met a Ben Mee cross after 58 minutes, but, having beaten his marker, glanced his header wide of Schmeichel's goal.
Chances were at a premium after the break with the quality in the final third lacking from both sides.
One chance fell to Burnley substitute Marvin Sordell, who very nearly caught Schmeichel out having been released behind the Leicester defence, but the Denmark goalkeeper was quick off his line and able to clear the danger.
Burnley continued to push for an equaliser and Jutkiewicz was inches away from his first competitive goal for the club on 74 minutes with a curling effort that flew just wide.
An injury to Kieran Trippier appeared to add to a disappointing day for Dyche's men when the full-back was carried off the pitch in the closing minutes with an ankle problem.
However, in the period of stoppage time added on because of Trippier's injury, Wallace placed his free-kick perfectly to beat Schmeichel and secure a point.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.