Lewis Hamilton's Mercedes team-mate Nico Rosberg managed 11 laps before suffering a wiring-loom problem, which needed to be modified overnight.
Max Chilton crashed following suspension failure in his Marussia.
The 21-year-old Englishman was unhurt after losing control during the afternoon at the end of the back straight. The team will do no further running until they have diagnosed the cause of the problem.
"This was the first pushing session of the day. We did one good lap and the car felt really nice and then coming down the back straight I was just about to brake and something gave way," said Chilton.
"I couldn't control it, I tried but I couldn't. It's unfortunate but I think the team know the issue and we should be back on the track tomorrow afternoon."
Despite McLaren's early problem, Button ended the day 0.848secs clear of Webber, who was less than 0.1secs ahead of Lotus's Romain Grosjean.
But the team will be concerned by the failure, which was in a part made by engine manufacturer Mercedes that has been modified over the winter in an attempt to prevent a repeat of the failure that caused Lewis Hamilton's retirement from the lead of the Abu Dhabi Grand Prix.
McLaren effectively lost the championship last season because of a series of reliability problems.
Button admitted the problem was "not ideal" but said he was encouraged by the feeling of the car.
"It's a nice starting point. Nothing stands out as a big issue, but lap times mean nothing right now," he said.
Massa described Button's pace-setting lap as "an incredible time" but indicated he felt he could have comfortably matched anyone else's laps if necessary.
Webber said the Red Bull "feels pretty good, so I'm happy".
Mercedes, meanwhile, are desperately trying to make up ground on the front-runners after ending last season struggling even to score points.
Rosberg's car briefly caught fire when the wiring loom failed and after investigating the problem the team realised they needed to stop running for the day.
New signing Hamilton is scheduled to have his first run in the car on Wednesday.
Rosberg said he was encouraged by his first proper run in the car, however brief.
"Very good, very positive," he said. "I can't say if it was quick or not, but feeling-wise I was comfortable. I could push, the balance was OK and it was very enjoyable to drive.
"I can guarantee you it will be a big step forward, but everybody else is also moving forward. We are hoping that we have closed the gap."
Williams's Pastor Maldonado - the only driver in a 2012 car, albeit with extensive 2013 parts on it - was ninth, ahead of Caterham novice Giedo van der Garde and Chilton.
FIRST PRE-SEASON TEST, DAY ONE, JEREZ, SPAIN, FASTEST TIMES
1. Jenson Button (GB) McLaren-Mercedes 1:18.861
2. Mark Webber (Aus) Red Bull-Renault 1:19.709
3. Romain Grosjean (Fra) Lotus-Renault 1:19.796
4. Paul di Resta (GB) Force India-Mercedes 1:20.343
5. Daniel Ricciardo (Aus) Toro Rosso-Ferrari 1:20.401
6. Felipe Massa (Brz) Ferrari 1:20.536
7. Nico Hulkenberg (Ger) Sauber-Ferrari 1:20.699
8. Nico Rosberg (Ger) Mercedes 1:20.846
9. Pastor Maldonado* (Ven) Williams-Renault 1:20.864
10. Giedo van der Garde (Ned) Caterham-Renault 1:21.915
11 Max Chilton (GB) Marussia-Cosworth 1:24.176
* = 2012 car