The 31-year-old Mexican added the IBF belt to his WBC, WBA and WBO straps in a winner-takes-all showdown at the MGM Grand Hotel in Las Vegas to unify all four major belts in less than 12 months.
Alvarez knocked Plant down twice in the 11th; the first time with a stinging left hook, followed up by a thundering right uppercut.
Plant got up but the American was still wobbly and in a fog as Alvarez chased him around the ring.
Alvarez pummelled Plant with rights and lefts to drop him for good at 1:05 of the round.
With a complete collection of 168-pound titles, he becomes only the sixth fighter since the WBO began sanctioning world title fights in 1988 to hold all four belts from the separate governing bodies at the same time.
"It hasn't been easy to get to this point," Alvarez said. "With my team I have gone really far.
"This is for everybody, especially for Mexico. We did it tonight. We are only six. It keeps me happy and motivated to be one of the six undisputed fighters in the world."
Only five other boxers - Oleksandr Usyk (cruiserweight), Bernard Hopkins (middleweight), Jermain Taylor (middleweight), Terence Crawford (super-lightweight) and Josh Taylor (super-lightweight) - have held all four belts at the same time.
Alvarez improved to 57-1-2 with 39 knockouts in handing Plant the first defeat of his career. Plant is now 21-1 with 12 KOs.
Alvarez won just about every round leading up to the 11th but still Plant proved to be an awkward opponent. Alvarez needed a spectacular KO to put a stamp on what up until then had been a mediocre performance.
“This fight itself was exactly as I envisioned it," Alvarez said. "The first few rounds, they were tough, but then it turned out just how we expected. We were able to execute our game plan, and we’re really happy with how it turned out."
Both fighters used the first round to feel each other out. They stuck to their game plans in the second round with Alvarez landing left hooks to the head and Plant sneaking in a few jabs.
Plant lost all but one round in the first half of the fight but he did a good job of staying out of trouble, slipping punches and weathering the coming storm. By the sixth round Plant's jab had lost some of its snap as his lack of power started to show.
Alvarez was warned for a low blow in the fifth but he also landed one of his best left hooks in the round right on the button that hurt Plant. He grew more confident as he started to realize that Plant couldn't hurt him with his now pawing punches.
In the 10th round, Plant got more careless and his jab completely disappeared. He tried to fight in close but couldn't get through Alvarez's stingy defence.
Halfway through the 11th Alvarez caught Plant with a vicious left hook and then followed it up right away with a right uppercut as Plant was going down.
Plant rose but it was clear the end was near. After a brief conversation with the referee the fight continued and Alvarez could smell blood. He went on the attack, charging forward and swarming Plant with a flurry of rights and lefts, finally putting on the finishing touches with a straight right to the head.
Alvarez said Plant, 29, wanted to keep going but he told him he should stop.
"He wanted to continue. I told him there is no shame. Of course I came out on top," said Alvarez.
“It was truly a historic night, and I’m so proud to be a part of it."