The Red Bull driver stormed past Hamilton in the closing stages of the season-ending race at the Yas Marina Circuit having benefited from a late safety car that bunched up the pack.
Hamilton appeared to be charging to glory, easily holding Verstappen at bay in the closing laps only for a crash for the Williams of Nicholas Latifi to change the course of events.
Confusion reigned as under-fire race director Michael Masi changed his mind to allow lapped cars to pass the safety car – meaning Verstappen had a clear run at Hamilton in the final lap and on much faster tyres.
The Dutchman broke into tears as he crossed the line, professing his love for his team and sitting by his car after bringing it to a stop: "This is unbelievable guys. Can we do this for another 10 to 15 years together," he said.
He told Sky Sports: "It's unbelievable. I kept fighting the whole race. I had the opportunity in the last lap. It's incredible, I'm still having a cramp. It's insane.
"These guys, my team, they deserve it. I love them so much. I've enjoyed working with them since 2016 but this year has been incredible."
For just the second time in the sport's history, the duo had gone into the race level on points at the top of the drivers' standings after going wheel to wheel for much of an enthralling season
Hamilton had looked on course for a record eighth championship after passing pole sitter Verstappen off the line.
The Brit started alongside his fellow title protagonist on the front row and was quicker off the mark, leading the race into turn one of the reconfigured track.
Those alterations were made to improve overtaking here and Verstappen attempted to take full advantage of the widening of the hairpin at turn seven as he lunged to try and regain his lead.
Hamilton went off the track as a result, rejoining having missed the turn but it was deemed he had no penalty to answer for as a season punctuated by collisions, near-misses and contradicting stewarding calls looked set for another twist.
The near-miss was all Hamilton needed to know he needed to scamper down the road to avoid any further incidents, aware that if he and Verstappen were both not to finish the title would go to his adversary by virtue of more race wins.
He was not to have it all his own way, however, as he came into the pits on lap 15 to avoid being undercut by Verstappen but emerged behind the sister Red Bull of Sergio Perez - who was given instructions to hold up Hamilton.
The Mexican did just that, costing Hamilton over six seconds as the tussled for the lead, Verstappen closing in and praising his team-mate as a "legend" over the radio.
Once clear, though, Hamilton once again showed his outright pace to start rebuilding the gap he had lost stuck behind Perez.
All seemed rosy until a virtual safety car was deployed to clear the stricken Alfa Romeo of Antonio Giovinazzi, with Verstappen pitting for fresh tyres as Hamilton stayed out.
Verstappen may have had the fresher rubber but Hamilton was still untouchable, Red Bull boss Christian Horner admitting the team needed a "miracle" with the gap at 11 seconds with 10 laps remaining.
And a miracle is exactly what Red Bull got as Latifi crashed into the barriers and brought out a safety car with just five laps remaining, Verstappen stopping for a third time and strapping on more new tyres.
Time, however, appeared to be on Hamilton's side as the laps ticked down behind the safety car and Masi opted to keep the five lapped cars between the leader and Verstappen in place.
He then changed tact, sending the quintet past Hamilton and the safety car meaning there was nothing between the title rivals as the pace car peeled off with just a single lap remaining.
Verstappen was ready to pounce and sprung, although Hamilton did battle back until he had nothing left to give.
As the unbelievable action unfolded on track, Mercedes team boss Toto Wolff fumed at Masi over the radio for his change in decision.
The two drivers shared a fist pump as they met ahead of the podium but with further messages broadcast from Wolff, it could yet be that an appeal is lodged against the call.