Khan flattened Vargas early on in the second, overwhelming the Colombian with his renowned fast hands.
The 31-year-old tried to finish things, pouncing onto Vargas after the count, but couldn’t capitalise on Vargas’ wobbly frame.
The round was petering out until 10/1 underdog Vargas caught Khan flush on the chin with a right hand, which sent to Brit to the canvas.
‘King Khan’ shot off his stool in the third and knocked down his opponent, though Vargas complained it was behind the back of the head.
In the fifth, Khan landed a flurry of sharp, accurate punches but the underdog astonishingly absorbed the blows without taking a knee.
Both fighters looked fatigued during the middle rounds, Khan decreasing in hand speed.
Vargas was on the front foot for rounds 9-10, prowling around the ring without particularly catching Khan too threateningly.
The closing rounds were much of the same, despite Vargas raising his hands in celebration after the bell.
The judges scored it 119-108, 119-109, 118-110 in favour of Khan, however, to deliver the Bolton fighter a win on his second comeback fight.
After the bout, Khan didn’t waste any time in pinpointing Manny Pacquiao as his next opponent.
“Manny Pacquiao is an amazing name in boxing. Who wants to see the Manny Pacquiao fight?” he said.
“I just want the biggest fights because that’s where I belong.”
When probed on the prospect of facing Kell Brook at 147lbs, the natural welterweight was less keen.
“Me and Eddie [Hearn] are going to have a sit-down. We’ll see where we go from there. I want to fight again at the end of the year – this was a great warm-up,” he said.
“The only fight that works for me over Kell Brook is Manny Pacquiao.
“Manny Pacquiao is who I want – I want Manny Pacquiao! He’s my number one pick.”