International Friendly: Colombia 3 Kuwait 1
The striker scored twice as Colombia hammered Bahrain 6-0 last Thursday and he continued a productive international break with an emphatic penalty in the 73rd minute.
There was more than an air of contention about the spot-kick, with the former Atletico Madrid man seemingly fouled by Musaed Al Enazi outside of the penalty area.
Falcao has endured a frustrating season on loan at Manchester United from Monaco, but his third goal in two games means he is just one goal shy of equalling Arnoldo Iguaran's record of 25 goals for Colombia.
Abel Aguilar's sensational volley put Colombia ahead, only for Al Enazi to bundle home an equaliser on the stroke of half-time.
Abdullah Al Buraiki struck the post for Kuwait shortly after the restart, but Colombia - ranked 122 places above their opponents in the FIFA world rankings - moved back ahead thanks to Edwin Cardona's strike from distance in the 68th minute, before Falcao's spot-kick wrapped up the win.
Colombia controlled possession in the early stages and fired the first warning when Falcao shifted the ball on to his right foot and shot wide of the right-hand post in the 10th minute.
Kuwait created little going forward, although Bader Al Mutawa did have tentative penalty claims waved away after going to ground from Carlos Sanchez's shoulder charge.
Colombia deservedly made the breakthrough in the 21st minute and in some style.
Juan Quintero's free-kick was only half cleared and Aguilar guided an exquisite side-footed volley into the bottom right-hand corner from 20 yards.
The South Americans remained in the ascendancy and Carlos Bacca also had the ball in the back of the net, only to be denied by an offside flag.
However, Colombia were hit by a sucker punch on the stroke of half-time when Al Enazi poked home Al Buraiki's corner.
The goal appeared to revitalise Kuwait, who started the second half at a high tempo.
Al Buraiki should have hit the target as he hit a wild shot over the crossbar when one-on-one, but the striker was desperately unlucky to see a fine left-footed effort from distance rebound off the right-hand post.
Colombia regained control thereafter and Cardona's accurate 25-yard drive nestled in the bottom left-hand corner with goalkeeper Hameed Youssef not reacting.
Pekerman's side were then afforded the chance to open a two-goal cushion when referee Sultan Abdulrazaq Al Marzouqi wrongly adjudged that Al Enazi had chopped down Falcao in the penalty area, with replays suggesting the contact occurred just outside the area.
Falcao made the most of the generosity as he thumped the resulting spot-kick into the top left-hand corner to secure a sixth straight victory for Colombia.