Moses opened scoring inadvertently for the European champions in the 12th minute from a corner taken by Frank Lampard. First viewing had suggested Branislav Ivanovic was the scorer but replays showed that the Nigerian had clearly headed the ball.
In the 35th minute, Moses surged into the box and cut back for Fernando Torres who left it for Frank Lampard and the midfielder passed to Ramires whose shot was saved.
Again in the 44th minute, off a break away he fed Eden Hazard for a one-on-one situation with Yann Sommer, who kept goal for Basel, but Hazard dragged his effort wide.
After Basel equalised in the 87th through a dubious penalty taken by Fabian Schar, Moses and John Terry combined to almost give the Blues the lead in the 92nd minute but Sommer made another brilliant save on the line.
Chelsea persisted and got the winning goal in the fourth minute of added time through a well taken free kick by Luiz.
Moses was rated the highest of all Chelsea players with a pass accuracy of 86% from 46 touches and he won 33% of his aerial duels. He committed one foul, had two shots and completed three dribbles successfully.
Moses has now averaged a goal every 110 minutes in Europe this season – the best goals per minute ratio for any Chelsea player.
His compatriot, Mikel Obi was on the bench for the duration of the encounter and the second leg is scheduled for next Thursday at Stamford Bridge.