Malesani, appointed earlier this week to replace Gian Piero Gasperini, saw his new side fall behind to a goal from Birkir Bjarnason in the 73rd minute.
But Diego Fabbrini levelled 10 minutes from time and a strong finale to the game gave the bottom side in Serie A hope of climbing to safety, even if the point still left them rooted to the foot of the table.
The early exchanges were typical of a relegation battle involving two sides from the bottom three.
Palermo, the home side, were too afraid of making mistakes to take any risks going forward while Pescara, who came into the game with a three-point advantage over their hosts, knew that a draw would be a positive result.
Only at the end of the first half did the hosts show any threat in front of goal, but Paulo Dybala laid bare their nerves by failing to take Fabbrini's inviting ball.
Pescara remained defensive, but a corner gave them the chance to take the lead in the 73rd minute.
Bjarnason showed strength and determination to emerge from within a group of players six yards from goal to head beyond the reach of Stefano Sorrentino and silence the Stadio Renzo Barbera.
The jeers and boos which greeted the goal seemed to spark Palermo into action.
Fabbrini chose the perfect time to open his Palermo account to bring the Sicilians level 10 minutes from time when he was left free at the far post to shoot into the far corner, despite not making the best contact with the ball.
It was all Palermo in the closing stages with and Ezequiel Munoz's volley was saved well by Mattia Perin.
With practically the last touch of the game, Pescara missed a glorious chance to take all three points when Emmanuel Cascione's cross was only just missed by Luciano Zauri.
Defeat would have been cruel on Palermo, who had spent the last 10 minutes camped in Pescara's half of the field.