The Portugal winger, on loan from Manchester United, controlled a throw in with his head and then unleashed a vicious, dipping shot which flew into the top corner, midway through the second-half.
The 28-year-old was overcome with emotion, clearly weeping as he was mobbed by his team mates
"It was a goal like any other," he told reporters. "I received the ball, saw the goal, shot and I was lucky."
"I thought about myself and everything that I have gone through," added Nani, who was born in Cape Verde and had a tough upbringing in Lisbon after his family emigrated to Portugal. "It's personal stuff, that nobody knows about."
Junya Tanaka had opened Sporting's account when he bundled the ball home with his thigh following a corner early in the second half.
Sporting are third in the table with 47 points, nine behind Benfica who beat Moreirense 3-1 away on Saturday. Second-placed Porto (49) face Boavista on Monday.
(Reporting by Brian Homewood; Editing by Greg Stutchbury)