The Monegasque, who started third in Bahrain and qualified second-fastest in Saudi Arabia, beat Red Bull to the top spot for the first time this season. It was also his third consecutive pole at the track.
The result came after Ferrari endured a difficult weekend in Australia, and in the aftermath of the news of the impending departure of sporting director Laurent Mekies, one of the key players at the Maranello outfit.
A change of philosophy on set-up had shown signs of promise in Melbourne, although the team didn't get it right in qualifying, and its weekend unravelled thereafter.
In Baku, things finally came together and it was rival Red Bull that faltered.
"I'm more than happy for everybody in the team because they've done very hard work over the last month," Vasseur told Motorport.com.
"And I think even under pressure we took some good decisions in terms of development and set-up, and it's paying off.
"I think it was also good in Melbourne, but we were not able to put everything together, and Charles did a mega job today.
"It's not an achievement, because quali is not an achievement, but it's a milestone into the season. A pole is always good for the confidence."
Vasseur admitted that the team was relieved that the car maintained the performance that was hinted at in Australia.
"You will never be able to draw a conclusion on one event," he said. "Melbourne was quite cold, and it's not a permanent track.
"For sure we did a step between Jeddah and Melbourne, it was quite obvious for us, it was quite obvious for the drivers. But still we had a doubt also because we didn't put everything together.
"But this weekend from lap one we were into the pace. OK, it's not the end of the weekend, and we didn't score points, but it's a good milestone for the team."
Ferrari also benefited from making the most of the single FP1 session, which was shortened by a red-flag period.
Unlike some rivals, the team opted not to bring a significant update package, other than low-drag Baku wings, to ensure that it would not lose time trying to optimise new parts.
"For sure I think on these kinds of formats, if you start with an issue on the balance, it's much more difficult to react," said Vasseur.
"Because you will carry the issue, long stint, short stint, then you will be completely blind for the weekend.
"We started in a good shape with the hard and the soft, and every single lap we were there. This is also giving confidence to the drivers."
Leclerc's team-mate Carlos Sainz had a less happy Friday, having had a couple of incidents, and the Spaniard will start Sunday's grand prix in fourth place.
"It started from Q1 when he spun and he burned one set," said Vasseur. "And then you have just one set in Q3, and it's putting you on the backfoot.
"I spoke with him after the session, and even for him somehow there is some positives in that we are going in the right direction, and he can take it for him elsewhere."
