Substitute Marc Bernal wasted a golden chance to put Barca ahead deep in first-half stoppage time before more controversy early in the second half.
Barca's Gerard Martin was shown a red card for an ugly challenge on Thiago Almada.
But, much to Atletico's anger, it was downgraded to a yellow after the referee was instructed to watch it again on the pitchside monitor.
The visitors piled forward in search of a winner, Musso producing a fine save to deny former Manchester City forward Ferran Torres before Lewandowski, 37, scored the late winner.
It came after Musso was unable to hold Joao Cancelo's attempt, the ball hitting Lewandowski on the shoulder and flying into the net.
"It's not easy to play here because the atmosphere and emotions are very high here," Barca boss Hansi Flick said after the game. "I am really happy with these three points.
"We need this hunger. We have to win the games. We have eight games to play. We have to stay focused and always be ready.
"We know that Champions League is totally different and every players has more to give. Everyone wants to be in the semi-final. We have three days more to prepare, to rest a little bit and focus on the next game. These are the kind of games why I do this job."
With eight games to go, Barcelona have 76 points while nearest rivals Real Madrid, who suffered a surprise defeat at struggling Mallorca earlier on Saturday, have 69.
The top two sides are due to meet on 10 May in Barcelona.
Atletico stay fourth on 57 points and will travel to face Barcelona on Wednesday in the Champions League quarter-final first leg (20:00 BST kick-off).