Webber's best time of 1:32.493s lap was 0.214s faster than Hamilton could manage, with the Mercedes-bound Briton sandwiched between the two Red Bulls. Sebastian Vettel was third, a further tenth back.
Nico Hulkenberg impressed once again for Force India, going fourth fastest, ahead of world championship leader Fernando Alonso and Romain Grosjean.
Last year's winner and this morning's pace-setter Jenson Button was seventh quickest, in front of Williams man Bruno Senna, Felipe Massa (who sparingly used the asphalt at Degner through the session) and Michael Schumacher - who crashed, but was unharmed, late on.
Grosjean was the first man to set down a marker, almost as soon as the green lights illuminated, with a 1:34.514s lap in the Lotus.
But with only six minutes in the books, the session was stopped as Paul di Resta put his Force India's two right wheels on the dirt on the entry to Spoon. The car then snapped around rapidly and he spun sideways into the barriers. The Scot was undamaged, the Force India less so.
"Completely down to me," he explained. "A bit ambitious a bit too early. Frustrating because I was six tenths up and Kimi [Raikkonen] was in my way, but the responsibility was mine."
Once the cars were back on track it was Alonso who shot to the top of the times with a 1:34.287s, which lowered the benchmark for the weekend so far.
That was never likely to last long though and Hamilton might have improved on it momentarily had he not locked up on the entry to the chicane.
While those two were squabbling, it was Button that whizzed to the front with a 1:34.150s, with Webber suddenly second on a 1:34.188s. Grosjean then had another crack at it and would have easily gone fastest but for one of his now customary entertainingly lairy moments - this time at the chicane.
As the session moved past the half-hour mark Vettel emerged on track, and impressively moved the hard tyre benchmark on with two laps that were faster than anyone had gone thus far, his best a 1:33.961s.
It was about that time that people started trying out Pirelli's softs.
Kobayashi was first to give them a go and went second quickest, within a hundredth of Vettel. But as more people switched to the soft tyre that duo rapidly dropped down the order, as first Button moved ahead, and then again Grosjean proved quick on a 1:33.107s.
Then it was Vettel's turn to give the yellow-monikered rubber a try and the world champion instantly went quicker still with a 1:32.826s. Hamilton's attempt was even better, but none were as fast as Webber, whose 1:32.493s would remain uncontested to the end.
It was an eventful session for several of the drivers.
Kimi Raikkonen spent much of the afternoon in the pits after his KERS battery overheated, began leaking and forced all the Lotus personnel in to rubber gear for safety reasons.
Rosberg required an engine change over the break after his car had ground to halt in the morning session, and Mercedes team-mate Schumacher was subject to a significant suspension change as the squad analysed some potential future tweaks.
The retiring legend then binned it at Spoon in a carbon copy of di Resta's previous indiscretion, though this time the race direction decided against a red flag.
The last 10 minutes of the session were devoted to long runs on the soft tyre, and unsurprisingly it was the McLarens and the Red Bulls that most consistently ran in the 1:39s.
The final twist in the session was the sight of Vitaly Petrov's Caterham parked in the Turn 1 gravel having apparently shed its rear wing on the straight, moments before the flag fell.