The Brazilian pair scored in either half for the French capital club to lift them to second in Ligue 1 behind Marseille, easing pressure on coach Laurent Blanc
PSG had drawn their three previous matches amid their worst start to a season since being taken over by the Qatar Investment Authority, but victory at the Stade Michel d'Ornano on Wednesday lifted them to second in Ligue 1, three points behind Marseille.
Along with Blanc, Moura has shouldered a significant amount of the scrutiny at the Parc des Princes so far this season, with former team-mate Jeremy Menez launching a stinging attack on the Brazilian on Tuesday.
But the diminutive playmaker slalomed past two opponents to give his side a first-half lead, before Marquinhos headed home the second after the break to settle the issue.
Injured duo Felipe Saad and Emmanuel Imorou missed out for Caen, while suspension and a heel problem respectively kept PSG pair Marco Verratti and Zlatan Ibrahimovic on the sidelines.
The latter's absence enabled Edinson Cavani to operate in his preferred central striker's role, and the big Uruguayan had the game's first opportunity early on.
Gregory van der Wiel cleverly worked his way down the right and crossed towards Cavani, who got in front of his marker but could only head straight at goalkeeper Remy Vercoutre.
Ezequiel Lavezzi hobbled off after 13 minutes, with 21-year-old Jean-Christophe Bahebeck replacing him, but that blow was soon soothed by a PSG goal.
Lucas received a Javier Pastore pass on the edge of the Caen box, employed rapid footwork to dribble past two opponents and slammed the ball into the back of the net from 10 yards.
PSG continued to dominate possession, but they were given a wake-up call 10 minutes before the break.
Julien Feret controlled the ball on his chest and volleyed a cushioned pass into the path of Jordan Adeoti, whose fierce drive from the edge of the box was tipped over by Salvatore Sirigu.
A Cavani dummy then set up Bahebeck, who failed to keep his strike down, before Vercoutre's legs repelled Lucas' shot.
Cavani had the final two chances of the half. First, his left-footed drive failed to trouble the Caen goalkeeper. Then, after a sublime piece of skill, the 27-year-old fired wide from close range.
Caen spurned a glaring chance to equalise within a few minutes of the restart.
A Herve Bazile cross from the left looped over Sirigu and found Mathieu Duhamel unmarked at the back post, but the 30-year-old somehow headed wide.
Bazile’s powerful shot from distance then forced Sirigu into a fine save, but just as Caen were gaining momentum, PSG doubled their lead.
Pastore whipped in a corner and though Ngolo Kante tried to clear Marquinhos' firm, downward header off the line, he only succeeded in diverting it into the roof of the net.
Marquinhos almost made it 3-0 with a header from another corner soon afterwards, but his effort went narrowly over.
Caen substitute Bengali-Fode Koita fired just wide from distance, before Duhamel's composure deserted him when well-placed.
Lucas went off to grand applause from the visiting supporters after 78 minutes, his contribution ultimately decisive.