Ferrari's Felipe Massa was fourth from Toro Rosso's Jean-Eric Vergne, Lotus's Kimi Raikkonen and Alonso.
Alonso also suffered a right-rear puncture on his penultimate lap of the session, which Ferrari spotted as he went past the pits into his final lap. He managed to get back to the pits.
Technical director Pat Fry said it happened "somewhere between the exit of Turn 13 and the start of Turn 14", which appeared to be where Vettel's also failed.
McLaren's Sergio Perez was eighth ahead of Hamilton's team-mate Nico Rosberg and the Force Indias of Paul Di Resta and Adrian Sutil.
"We don't know what happened yet," said Vettel. "I lost the rear right very suddenly. We need to have a look. At the moment we are trying to understand. Other than that it was a positive day.
"Rain is very likely on Saturday and Sunday, the question is when, how much and where. We had a look at the car. But both of us seemed pretty happy with what we had."
The two Red Bull drivers were very closely matched - Vettel was just 0.059secs quicker than Webber - but they achieved them in different ways.
The team were assessing different levels of downforce on their cars.
Vettel was running with lower downforce, which gives faster straight-line speed in the first and final sectors of the lap but costs speed in the middle sector, which is a series of quick corners.
Belgian Grand Prix weather forecast
Webber ran a higher downforce set-up, which produces the opposite effect.
Vettel was about 0.4secs quicker than Webber in both the first and third sectors, while the Australian was 0.8secs quicker than the German in the middle sector. That combined to put Vettel just 0.059secs ahead.
Red Bull have traditionally run their car with a higher downforce set-up, optimised for ultimate lap time, but this philosophy has been based on their ability to qualify consistently at the front.
The qualifying pace of the Mercedes cars, which have been on pole for six of the last seven races, and the long straights at Spa which facilitate overtaking have forced them to reconsider that approach.
Ferrari also took a split approach, converting Alonso's car away from the low-downforce set-up used by Massa after the first runs of the session.
He then moved up to seventh from out of the top 10, but did not do a race-simulation run late in the session.
Red Bull, meanwhile, looked as impressive over a series of laps on high fuel levels as they did on their one-off laps.
Saturday 24 August : Final practice at 09:55 BST on BBC Two, plus live text commentary online. Qualifying at 12:10 BST on BBC One plus live text commentary online
Belgian Grand Prix, day three
Sunday 25 August: Race coverage at 12:10 BST on BBC One & BBC Red Button at 13:00 BST, Radio 5 live, plus live text commentary online. F1 Forum, 15:15 Connected TV. Highlights, 19:00 BBC Three & BBC Red Button
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