Four minutes after he went on, Brescianini finished off a counterattack set up by Nicolo Zaniolo and Ademola Lookman in the 88th minute of Saturday's match.
Fisayo Dele-Bashiru scored midway through the first half for Lazio after receiving a ball over the top and blasting past onrushing goalkeeper Marco Carnesecchi.
The draw left Bergamo-based Atalanta just ahead of second-placed Inter Milan, who won at Cagliari 3-0 earlier and also have a match in hand.
Atalanta face Inter in their next match on Thursday, in the semi-finals of the Italian Super Cup in Saudi Arabia. Juventus play AC Milan in the other semi-final.
Atalanta were without leading scorer Mateo Retegui, who injured his left leg against Empoli last weekend.
Since a 1-0 loss at Bayer Leverkusen in the Champions League this month, Serie A defending champions Inter Milan have been perfect, scoring 13 goals while conceding none for four wins.
Inter's latest performance was decided with two assists from Nicolò Barella.
Alessandro Bastoni put Inter ahead with a looping header following a cross from Barella after the break.
Lautaro Martinez scored his first Serie A goal in nearly two months by volleying in another cross from Barella.
Then Hakan Calhanoglu converted a penalty.
Earlier, Patrick Vieira's Genoa won at Empoli 2-1 with goals from Milan Badelj and Caleb Ekuban; and Parma beat last-placed Monza 2-1 with a header from Lautaro Rodrigo Valenti eight minutes into stoppage time to spoil the debut of new Monza coach Salvatore Bocchetti.
