Fernando Alonso described McLaren's performance on day three of pre-season testing as a "big step forward".
The double world champion was hampered by an engine water leak after 32 laps but the team finally put some mileage on their new Honda-powered car.
Sauber's Felipe Nasr set the fastest time, as world champions Mercedes and Red Bull also suffered engine problems.
McLaren had been in desperate need of some track time in Jerez in order to put the new MP4-30 through its paces.
Until Tuesday, they had managed just 17 laps over four days of testing, spread over a post-season outing in Abu Dhabi in November and the first two days in Jerez.
Alonso's fastest time was set in damp conditions before the track dried out, so the fact that it was 12 seconds off the fastest of the day was irrelevant.
When he was on the circuit, he spent some time close to Nico Rosberg's Mercedes and was not far off its pace.
"For what it's worth, the MP4-30 looked well balanced during a 10-lap run late-morning," said BBC F1 pit-lane reporter Tom Clarkson. "On a damp track, it didn't lose much to Rosberg."
The water leak forced Alonso to abort a run early in the afternoon, ending McLaren's action for the day.
But the team are confident any broken components can be replaced in time for tomorrow's final day of testing.
Rosberg's day was temporarily halted by an engine shutdown but the team had the German back out again within an hour.
He ended up completing 151 laps, to add to the 157 he did on day one and the 91 logged by Lewis Hamilton on day two.
Kimi Raikkonen had his first experience of the Ferrari after team-mate Sebastian Vettel spent the first two days out on the track. The German set the fastest time on the opening two days.
Raikkonen, the 2007 world champion, was quick throughout Tuesday and set the pace in the morning session. He ended up second fastest at the end of the day.
Daniel Ricciardo managed only five laps in the Red Bull during the morning before engine problems forced a lengthy spell in the pits.
But he returned to the track in the afternoon, ending up seventh fastest, behind the Williams of Felipe Massa, the Lotus of Pastor Maldonado and Toro Rosso novice Carlos Sainz Jr. Alonso was slowest of all.
Headline times in pre-season testing are notoriously unreliable indicators of form as it is impossible to know the specification in which the teams are running their cars.
Fastest lap times, day three of first pre-season test in Jerez
1 Felipe Nasr (Brz) Sauber-Ferrari 1:21.545
2 Kimi Raikkonen (Fin) Ferrari 1:21.750
3 Nico Rosberg (Ger) Mercedes 1:21.982
4 Felipe Massa (Brz) Williams-Mercedes 1:22.276
5 Pastor Maldonado (Ven) Lotus-Mercedes 1:22.713
6 Carlos Sainz Jr (Spa) Toro Rosso-Renault 1:23.187
7 Daniel Ricciardo (Aus) Red Bull-Renault 1:23.901
8 Fernando Alonso (Spa) McLaren-Honda 1:35.553