Blaise Matuidi was also on the scoresheet as the reigning champions picked up three points that see them climb above fellow big spenders Monaco to the top of the league table.
An uneventful opening 30 minutes to the contest was ended when Zlatan Ibrahimovic, having just fired a 25-yard free kick high into the stands, found Matuidi with a superb through-ball.
The midfielder shot low past Cedric Carrasso and then won the sprint against the home keeper to ensure that the ball dribbled over the goal line.
Claudio Ranieri's side then began to turn their 60% of possession into chances and, after Ibrahimovic came close, Moura netted his team a second following a marvellous piece of individual skill.
The Brazilian international controlled a long ball from Marco Verrati before advancing into the box, brilliantly feigning to shoot, before slotting past the outwitted Carrasso on 64 minutes.