The Red Bull driver had a poor getaway from pole position and lost the advantage to Ferrari's Leclerc, who began to open up a clear advantage at the front after an early safety car period.
But Leclerc's fortunes turned when he began suffering graining on his right front tyre, and his pace fell away.
That handed the advantage back to Verstappen, who pushed hard to get himself within DRS range before making a move in to Turn 2 on the penultimate lap.
Verstappen said that once it became obvious that Leclerc was struggling, it was just a matter of finding the right moment to make his move.
"Charles was definitely struggling more with the graining," said Verstappen. "Then of course, I could close up and use the DRS to get by.
"But I think it was more just of a bit of a waiting game, because every lap it seemed like the gap or the difference between the two cars was getting bigger in terms of a lap times."
Despite his tyre advantage though, Verstappen admitted it took some effort to get within striking range.
"Of course, at one point, it's very tricky once you get around that one second window to get super close," he explained.
"Of course with these cars, it is better to follow. But it's still very hard to pass. You still need to use the tyres and especially with the deg we had on the soft, getting in that DRS window, it was hard.
"But then once I got into it, I think on the second attempt we had a good little battle into Turn 2. But yeah, clearly, we had a bit more pace at the end of the race."
The F1 world champion said he needed to analyse exactly what went wrong at the start, as too much wheelspin led to a poor getaway.
"[The start was] terrible. When I let the clutch go, just a lot of wheel spin and no traction. So my start was very, very poor," he said.
Asked if the fact he was starting from the dirty side of the track could have been a factor, Verstappen said: "I mean Lando had a decent start, so there's no excuse.
"My start was just terrible. I didn't have gear sync for whatever reason. So, yeah, I need to see exactly what went wrong."
