Falcao had not started for Jose Pekerman's side since November 19 last year, when Colombia played out a goalless draw against Netherlands, after damaging his anterior crucial ligament while playing for Monaco in the Coupe de France in January.
The serious knee injury forced Falcao to withdraw from Colombia's World Cup campaign but the 28-year-old striker made his long-awaited return start in typical fashion.
Falcao - wearing the captain's armband - rose highest to head home a seventh-minute opener at Red Bull Arena - becoming Colombia's second all-time leading goalscorer with 21 in 52 appearances.
Strike partner Carlos Bacca bagged a quick-fire brace in the second half as Colombia outclassed their opponents to end a two-game losing streak.
Colombia were dominant from the outset, pinning El Salvador into their own half for most of the opening stanza in New York.
And it took just seven minutes for the Colombians to turn their possession into goals, with captain Falcao breaking the deadlock.
Falcao, who scored his first Manchester United goal last week, got on the end of an inch-perfect cross from Santiago Arias, directing a powerful header past El Salvador goalkeeper Henry Hernandez.
While Colombia were clearly superior, El Salvador, however, did have a good opportunity to draw level five minutes before half-time through Marvin Monterrosa.
Monterrosa made a darting run, unmarked, between two defenders but Arias made a last-ditch block as Colombia preserved their lead at the break.
Bacca netted two goals in as many minutes as Colombia continued where they left off in the second half.
The Sevilla striker scored his first following a goal-line scramble after two initial efforts were blocked in the 49th minute.
And he was at it again two minutes later, tapping home from inside the six-yard box after Falcao poked the ball into his path.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
