Verstappen sacrificed track position early in exchange for ending the race on the quickest strategy, but Hamilton turned in one of the defensive drives of his career in an arguably slower car for his first season-opening win in six years.
The Briton was racing with laps 10 laps older than the Dutchman’s when they met on track with six laps to go, and a lockup at turn 10, sending him wide off the track, seemed a certain portent that his defence was to be in vain.
Verstappen help up his part of the prophecy with three laps to go when he swept around the outside of the Mercedes at turn four, but he put all four wheels off the track to get the pass done and was forced to hand the place back later that lap.
The 23-year-old kept the pressure up in pursuit of his 11th victory and started the final lap less than a second adrift, but the seven-time champion had found his defensive rhythm despite his dilapidated tyres and crossed the line by a hard-fought 0.745 seconds.
“What a difficult race that was!” Hamilton said. “Max was all over me right at the end, but I just about managed to hold him off.
“It was one of the hardest races I’ve had for a while.
“We love the challenge, I love the challenge - I still love what I do.”
Verstappen was disappointed to snatch defeat from the jaws of victory but took heart from the fact his car was more than a match for the Mercedes.
“It’s of course a shame, but you also have to see the positive,” he said. “We are really putting the fight onto them, and I think it’s great to start the year like that.
“Overall we managed to finish the race and score good points.”
Valtteri Bottas finished third in the sister Mercedes. The Finn was disappointed not to be given a more creative strategy to fight for the lead despite falling off the pace early in the race, but a late tyre change at least secured him a bonus point for fastest lap.
“Disappointing for sure,” he summarised. “The good thing as a team is we got good points, but from my side it felt like for me, strategy wise, we were on the defensive side instead of attack, which I was quite surprised by.”
Lando Norris secured a strong fourth place after picking up three places in the opening phase of the race, including that of new teammate Daniel Ricciardo on the first lap.
New Red Bull Racing recruit Sergio Perez salvaged fifth after a difficult weekend. He qualified 11th and started from pit lane after an electrical problem on the formation lap, but the Mexican was relentless in his progress, including three passes in the final 16 laps, to end the weekend on a high.
Ferrari’s Charles Leclerc beat Daniel Ricciardo to sixth by seven seconds, with new teammate Carlos Sainz just a second further adrift in eighth.
Japanese debutant Yuki Tsunoda was superb for AlphaTauri to score two points despite running 16th after five laps, capping off his race by demoting Aston Martin’s Lance Stroll to 10th.
Stroll’s teammate Sebastian Vettel had a difficult debut for the British team, rear-ending Alpine’s Esteban Ocon in a botched defence of 12th place and copping a 10-second penalty, while Fernando Alonso’s return to the sport after a two-year hiatus ended with a brake problem after 33 laps.