Hamilton dominated qualifying to start from pole position, but he had his way eased pre-race when Verstappen and Valtteri Bottas were demoted to seventh and sixth respectively for ignoring yellow flags during qualifying.
A clean getaway was then all he needed to take the lead on the first lap, and with only slower cars immediately behind him, he was able to control the pace of the grand prix and grind out a straightforward victory.
“It was pretty lonely at the front,” he said. “I enjoy those races when you’re battling through, but we needed those points today, so a real solid job from the team.
“To get back-to-back wins is a great feeling and sets us up well for the final two races.”
Verstappen recovered rapidly from his penalty, resuming second place after just five laps, but Red Bull Racing had no answer to Mercedes pace, with even a pair of early pit stops failing to shake the lead from Hamilton’s grasp.
The final phase of the grand prix descended into a battle for the fastest lap of the race, with the title protagonists trading times until a pit stop with two laps to go for soft tyres secured the bonus point for Verstappen, limiting the damage to his championship lead.
“At the end of the day to get the fastest lap was very nice,” he said. “It keeps it exciting.
“I feel good. It’s going to be a tight battle to the end.”
But as much as Qatar was another critical chapter in the championship battle, Fernando Alonso stole the show with his first podium finish since 2014 and the first of his F1 comeback.
Alonso was promoted to third on the grid behind Hamilton and Pierre Gasly after Verstappen and Bottas’s penalties and turned in a sizzling first lap to slingshot himself into second place around the outside of turn two.
His Alpine car had the pace to keep the AlphaTauri behind, but he also had the strategic flexibility of starting with the medium tyre, whereas Gasly had the soft. It forced the Frenchman into a two-stop race, whereas the Spaniard was banking on a single stop.
It left him vulnerable not to Gasly, whose challenge faded after his second pit stop, but to the recovering Valtteri Bottas and Sergio Perez, who spent the early part of the race cutting through the midfield.
Bottas assumed third at half distance, but a tyre failure on lap 33 took the Finn out of the running and eventually forced his retirement, leaving Perez on a two-stop race to chase down Alonso in the final stint for a photo finish.
In the final 15 laps the situation was becoming critical, with three more tyre failures among the midfield highlighting the difficulty of Alonso’s challenge, but a two-lap virtual safety car with three laps to go earnt him an important breather that allowed him to hold back the charging Mexican by just 2.8s in a perfectly judged race.
“Unbelievable,” he said. “Seven years, but finally we got it.
“With Checo it was very close at the end, but I’m so happy for the team.
“I think it was quite well executed, the race.”
Alonso’s result along with fifth for teammate Esteban Ocon broke Alpine 25 points clear of AlphaTauri in the battle for fifth in the championship standings.
Perez finished a disappointed fourth, though his points haul and Bottas’s retirement brought Red Racing to within five points of Mercedes on the constructors table.
Ocon held back Aston Martin’s Lance Stroll to secure fifth ahead of the Canadian.
Carlos Sainz and Charles Leclerc were seventh and eighth for Ferrari, outscoring lone McLaren scorer Lando Norris in ninth to take their team 39.5 points clear for third in the standings, while Sebastian Vettel collected the final point of the race with 10th.