After the ninth leg of the 22-race season, Verstappen's lead in the Formula 1® drivers' championship stands at 46 points, and that is because his Red Bull team-mate and closest rival in the standings Sergio Perez was an early casualty in Montreal.
Sainz, in the Ferrari, clung tight behind Verstappen over the closing laps after a lengthy safety car delay but could not quite forge an overtaking opportunity.
That meant Verstappen's 150th grand prix was a triumphant one, as Sainz was kept waiting for his first F1® victory.
Hamilton had not finished on the podium since the season-opening race in Bahrain, a wait of seven races, so the Briton was delighted to get third, ahead of Mercedes team-mate George Russell. Hamilton said it was "quite overwhelming".
Perez, who crashed out in Q2 on Saturday, pulled over to the side of the track and abandoned the race on lap nine, seeming to lose power and complaining of being stuck in gear.
It was clear that Fernando Alonso, in the Alpine, would not be able to convert second place on the grid into a top-three finish as the two-time champion gradually drifted down the field.
Leclerc first went to the pits on the 42nd lap, but it was a painfully sluggish stop and left the man from Monte Carlo down in 12th place. It was a credit to him and his team that he was able to surge through the field and close into just three points behind Perez in the championship.
Yuki Tsunoda crashed out on lap 49 and that forced the drivers to proceed behind the safety car for five laps, drawing the field tightly together.
Leclerc, who started on the back row of the grid after his car was fitted with an all-new power unit, jumped ahead of the Alpines of Alonso and Ocon to go fifth, while at the front, Verstappen fittingly showed the defence of a champion to fend off Sainz.
It's the pits for Perez
Trailing Verstappen by 21 points coming into this race, Perez was at least looking to tighten his grip on second place in the championship, so Sunday's early exit was a shocker for the Mexican. It compounded his miserable weekend after he accepted it was driver error that caused the crash in qualifying that forced him to settle for 13th on the grid.
Leclerc, third in the standings, made a 10-point incision into the 13-point pre-race gap between the pair. Both are well adrift of Verstappen, though, and it will take something remarkable to reel in the reigning champion from this point.
Seventh heaven for Red Bull
Building on last year's breakthrough title for Verstappen, this has been Red Bull's best start to an F1® season, with this the seventh win in nine races for the team (six wins for Verstappen, one for Perez). They won six of the first eight in 2011 as Sebastian Vettel dominated, but then went three races without a victory.
IN THE POINTS
1. Max Verstappen (Red Bull)
2. Carlos Sainz (Ferrari) +0.993s
3. Lewis Hamilton (Mercedes) +7.006s
4. George Russell (Mercedes) +12.313s
5. Charles Leclerc (Ferrari) +15.168s
6. Esteban Ocon (Alpine) +23.890s
7. Fernando Alonso (Alpine) +24.945s
8. Valtteri Bottas (Alfa Romeo) +25.247s
9. Zhou Guanyu (Alfa Romeo) +26.952s
10. Lance Stroll (Aston Martin) +38.222s
1. Max Verstappen (Red Bull) 175
2. Sergio Perez (Red Bull) 129
3. Charles Leclerc (Ferrari) 126
4. George Russell (Mercedes) 111
5. Carlos Sainz (Ferrari) 102
1. Red Bull 304
2. Ferrari 228
3. Mercedes 188
4. McLaren 65
5. Alpine 61
Silverstone awaits in two weeks' time, and could Hamilton be even more of a threat there? Leclerc will certainly hope his own troubles are in the past, and that could make for a gripping British Grand Prix on July 3.