Figo, 36, secured the win in the second half, heading home a cross from Davide Santon, a young defender who is just half his age, while Stankovic made it 3-0, also with a header.
As Inter pressed ahead from the start, Stankovic missed an early chance, heading over an inviting cross from Ibra, but Inter had to thank their Brazilian goalkeeper Julio Cesar for a prodigious save that prevented a Lecce equaliser in the 18th minute.
Defender Guglielmo Stendardo was left unmarked at the far post and aimed a good downward header, but saw Julio Cesar dive to push the ball away.
The southern-Italy hosts pushed immediately after the break but Figo made the game safe in the 71st minute and Stankovic made it 3-0 with eight minutes to go to move Inter on to 53 points from 23 games.