The Bergamaschi were the better side at the Stadio Atleti Azzurri d'Italia but could not find a way past Lecce goalkeeper Julio Sergio, although both Guido Marilungo and Federico Peluso struck the woodwork.
The result left Atalanta in 15th place, six points clear of third-bottom Lecce.
Atalanta have found the net just twice in their last five encounters but they started well and almost went ahead in the 21st minute when a bad pass by Lecce defender Massimo Oddo gave the ball to Marilungo.
He surged inside the area and fired a diagonal shot that hit the far post.
Two minutes later and Matias Schelotto's cross towards the far post found Peluso and he smashed the ball onto the post.
Atalanta continued to press forward and in the 36th minute, Julio Sergio kept out Peluso's close-range header from Marilungo's cross.
Before the break, Julio Sergio also did well to save German Denis' 10-yard strike.
Lecce came to life in the second half and almost went in front in the 48th minute but Valeri Bojinov somehow missed the target from just five yards out.
Shortly after the hour mark, Atalanta goalkeeper Ciro Polito made his first save of the afternoon when he parried away Luis Muriel's powerful drive.
Peluso then nodded Maximiliano Moralez's cross wide.
Julio Sergio did well to clear substitute Manolo Gabbiadini's powerful free-kick with six minutes to go as Lecce held on for a share of the spoils.