The German was the cause of one of eight red flags for drivers stopping out on the track.
McLaren's day ended with Button stopped out on track, but they will be hugely encouraged by the mileage done by their car.
The second Red Bull driver Sebastian Vettel was only 20th overall after stopping out on track with an electrical problem after just four laps.
He managed to get out on to the track again for the final 13 minutes of the day but his running was cut short five minutes before the scheduled end when English rookie Max Chilton's Marussia stopped out on track.
Di Resta's team-mate Nico Hulkenberg was knocked out in the first session after his car stopped out on the track at the first chicane before he had recorded a timed lap.
The redesigned part was fitted for Saturday, but Button stopped out on track after just over an hour's running and managed only 12 laps in total in the morning.
The day's activities in southern Spain ended five minutes early when Button's car stopped out on the track as McLaren ran it dry - a standard procedure for teams to evaluate how well their fuel pick-up system is working.
Following Webber's difficulties in qualifying in China, when the car stopped out on the track and was later found not to have enough fuel in it to provide the required sample, there were suggestions the issue had conveniently ensured Webber was kept away from Vettel in the race.
