The Briton has now gone a record 33 successive races in the points. "Then I ended up with nowhere to go".
It wouldn't matter, however, as the German made his way much better through the midfield pack as overtaking into the two chicanes and at Turn 11 proved easier than expected.
Vettel now trails Hamilton, who won the race comfortably, by 14 points in the drivers' standings.
"The new engine feels clean and fresh", said Hamilton. Vettel was investigated for causing a collision and given a five-second time penalty by the stewards.
It was Hamilton's 65th career win.
Eventually, Verstappen and Ricciardo would pit from second and third and would emerge either side of Vettel, who ran fourth for a short time. Only Michael Schumacher has more victories with 91.
Sebastian Vettel managed to finish fifth after a collision at the first corner saw him damage his auto and incur a five-second time penalty.More news: Apple to fix 'sticky' keyboard problems for free
Al-Hamad drove a race-winning 2012 Lotus Renault E20, which Raikkonen, then with Renault, drove to victory in Abu Dhabi in November 2012.
The incident dropped both to the back of the field after pitstops while the safety auto was deployed for four laps with debris scattered across the track from other accidents. "Obviously today, I would have loved to have a different result but we move on". "There are no more negotiations in progress", Hamilton, 33, added. "We're all on the edge, we're fighting for the world championships, we're not pootling around, we're out there putting our lives on the line, we're out there putting the cars as far beyond the edge as we can in the safest manner. We are not twiddling around".
Kimi Raikkonen was sixth in the second Ferrari ahead of Carlos Sainz of Renault, Charles Leclerc of Sauber, Kevin Magnussen and his Haas team-mate Romain Grosjean, who crashed during the top-ten shootout, halting the session for eight minutes.
"But my race was lost at Turn 1".
There was gloom at McLaren, with last weekend's Le Mans 24 Hours victor and double world champion Fernando Alonso only 16th. Hamilton had not been troubled at the front of the race, he managed and maintained the gap to Verstappen to ensure a clinical finish.
Driving conditions were optimal at the 5.8-kilometer (3.6-mile) circuit situated just inland from the Cote d' Azur.
The return of the French GP is the first part of an unprecedented tripleheader of three races on consecutive weekends.
With less time for Ferrari's engineers to play catch up, Hamilton will hope to press his advantage at the Austrian and British races to open up a commanding lead in the championship fight.