The switch to ground-effect cars last year heralded a lean period for Hamilton and Mercedes, with the seven-time world champion going without a win since 2021 and having to wait 33 races before qualifying on pole again.
Having ended Friday's practice session with his car feeling "at its worst", Hamilton topped FP3 on Saturday morning before going on to beat Max Verstappen by 0.003 seconds on his final lap of Q3 to claim his 104th career pole.
Speaking in parc ferme after qualifying, Hamilton admitted he "didn't expect" to be in contention for pole and had "nothing left in it" come the end of the lap.
"It's been a crazy year and a half," Hamilton began.
"So, I've lost my voice from shouting so much in the car. It's amazing, that feeling. I feel so grateful to be up here because the team have worked so hard.
"We've been pushing so hard over this time to finally get a pole, it just feels like the first time.
"And a big, big thanks to the crowd here. We have such an amazing crowd every year here in Budapest.
"I didn't expect coming today that we would be fighting for pole. So, when I went into that last run, I gave it absolutely everything. There was nothing left in it."
Source: Autosport