Monaco returned to the Ligue 1 summit following a patchy 1-0 win over Lorient on Sunday.
Having been displaced on Friday night by champions Paris Saint-Germain, and then passed too by Saint-Etienne on Saturday, Monaco needed a win in the Principality to take over top spot again.
And record signing Falcao was the match-winner, slotting home cooly from the spot on six minutes after he himself had been brought down in the area by Lorient goalkeeper Fabien Audard.
It wasn't an always convincing performance by the big-spending Russian-backed club, who were guilty several times of over-playing the ball and trying to walk it into the net.
And Monaco's Italian coach Claudio Ranieri could not hide his displeasure.
"I was a bit annoyed at the end of the match because the match was calm and we complicated matters at the end," he said.
"It's very important to know how to hold onto the ball when leading 1-0, you need to know how to wait for the right moment.
"(But) we played well in the first half. We were motivated."
Their breakthrough came early on when Falcao tried to round Audard, who brought down the Colombia forward and earnt a booking for his troubles.
Lorient were not overawed by their opponents, despite finding possession hard to come by as Portugal international Moutinho ran the show in the middle of the park for the hosts.
Yet the visitors created several scoring opportunities, only for a wayward display by Guinean striker Abdoulaye Sadio Diallo, who was hauled off seven minutes before half-time, to cost them.
Sadio Diallo swiped wildly at thin air after dashing into the box before hurriedly going for goal, yet succeeding only in connecting with the ball with his planted foot, thus taking it out of range of his swinging one and falling flat on his back.
Up the other end, Falcao was inches away from doubling his and Monaco's tally but he slid in a fraction too late onto a whipped delivery from the left by marauding full-back Layvin Kurzawa.
Lorient had the ball in the net on 26 minutes but it was justly chalked off as Sadio Diallo had strayed half a yard offside as he knocked home Maxime Barthelme's pinpoint cross from the left.
Monaco went close again on 36 minutes as Lamine Kone bounded down the overlap and thrashed a shot against the upright.
Falcao wasted a fine opportunity 11 minutes into the second period when one-on-one with Audard, but instead of shooting first time he tried to dribble the goalkeeper and was crowded out by backtracking defenders.
Later Sunday, Nice continued their climb up the table with an impressive 2-0 success at Lille.
Argentine striker Dario Cvitanich bagged both goals in the first half with crisp right-footed finishes from similar positions.
Nice, who began the season with a 4-0 defeat at Lyon followed by two draws, moved up to sixth while Lille dropped to 11th.
Saint-Etienne are second after their 3-1 win at Valenciennes on Saturday.
Benjamin Corgnet grabbed a brace either side of Romain Hamouma's strike for Les Verts before Maor Melikson scored a consolation for the hosts from the penalty spot 10 minutes from time.
Blaise Matuidi and Lucas Moura were on target for PSG on Friday night in their 2-0 win at Bordeaux that leaves them in third, just ahead of Marseille, who were held to a 1-1 draw at Toulouse.
Sochaux are rock bottom following their 1-0 reverse Saturday at Nantes.