A week ago in Germany it was Button who led the way from Hamilton as McLaren hit the ground running at Hockenheim, with their cars sporting a raft of new upgrades.
Considerable improvement was made in Germany, only for heavy rain in qualifying to compromise their starting positions as the team discovered to their horror a lack of performance in the wet.
With Button sixth and Hamilton seventh on the grid, the former was able to challenge for the victory, finishing third which was converted to second following a post-race penalty for Red Bull's Sebastian Vettel.
For Hamilton it was a 100th grand prix to forget, the 27-year-old retiring 10 laps from home with damage sustained from a lap-two puncture, but there was enough performance in the car to offer up hope for this weekend.
Under clear blue skies at the Hungaroring, and with air and track temperatures at 26 and 37 degrees respectively, the British duo were comfortably quickest in the opening 90 minutes as again dry conditions suited the car.
Hamilton topped the timesheet with a lap of one minute 22.821secs around a circuit renowned for being tight and twisty, finishing 0.101secs clear of Button.
Ferrari's Fernando Alonso, now 34 points clear of Red Bull's Mark Webber at the top of the season standings after his win in Germany, was the nearest challenger but over half a second behind Hamilton.
Mercedes duo Nico Rosberg and Michael Schumacher were fourth and sixth, the seven-times champion a second down, sandwiching Romain Grosjean in his Lotus.
Ferrari's Felipe Massa and Lotus' Kimi Raikkonen were just behind Schumacher, with Williams' reserve Valtteri Bottas again putting in another solid Friday morning outing to finish ninth, 1.331secs down.
Webber and Vettel were 13th and 15th, but with the duo opting for heavier fuel runs and with much more to come, with Force India's Paul di Resta in 14th and complaining of his car being difficult to drive.
At the bottom, HRT reserve Dani Clos - standing in for Narain Karthikeyan - was 5.355secs behind Hamilton and just over a second down on team-mate Pedro de la Rosa.