Hamilton, coming off a victory in the German GP, shaved more than two seconds off his pace-setting morning session lap after completing the Hungaroring circuit in 1 minute, 21.018 seconds in the second stint.
The McLaren driver, a two-time winner in Budapest, was more than two-tenths of a second quicker than Ferrari's Fernando Alonso.
"It's a great feeling to already start on a high -- it wasn't really expected. The climate is working for us; it's not quite as hot as it usually is here," Hamilton said. "It's early to say what's going to happen but we can compete with the guys in the front."
Sunday's 70-lap race is the last before F1's four-week summer break. Practice wraps Saturday before qualifying.
McLaren and Ferrari continued to close the gap on constructors' leader Red Bull, which dominated the championship with seven wins in the first eight GPs but has seen its main rivals share the past two victories.
McLaren can be optimistic after winning three of the past four Hungarian GPs, while climbing temperatures also could help Ferrari. Rain is expected to hold off Saturday when Red Bull's perfect grip on qualifying will come up against its sternest test. The Austrian team has started from pole position in each race this year and 25 of the past 29 races.
"Every time we get into qualifying they pull something out," Hamilton said. "I think we have the same pace as we did last week. We do have a positive buzz in the team."
Vettel, the defending F1 champion coming off a season-low fourth place at the Nuerburgring, leads the championship with 216 points. Webber is second with 139, Hamilton has 134 and Alonso 130. Button remains with 109 points after retiring from the past two races.
"McLaren and Ferrari are very quick so I think we need to raise our game to make sure that we will find ourselves at the top as well," Vettel said.