Massa, who moved from Ferrari at the end of last year, completed 99 laps in the Mercedes-powered FW36 car and set the fastest time yet in seven days of testing at the Sakhir desert circuit.
"I'm really happy with the car and feel we found a good balance," said the 32-year-old, who carried out a full qualifying simulation on supersoft tyres towards the end of the afternoon.
"You can never be sure that you are 100 percent ready for the first race but I feel that what we have done in these days testing has been important for making sure that we have a car that can not only get to the end of the race but that will have good performance as well."
Vettel's car broke down with an electrical problem on its first lap out of the garage. He tried again later but only made it to the end of the pitlane before stopping again.
The German then helped marshals push it back to the Red Bull mechanics, who diagnosed a leak that had also damaged other parts.
"It's not the best situation to be in but we can't change it," said the 26-year-old. "Everybody is extremely motivated to fix it but it doesn't happen overnight.
"At this stage obviously reliability is still a big question mark. It's difficult to say how long it will take to remedy."
The season starts in Melbourne on March 16 and reliability is the key concern for teams facing the biggest technical upheaval in a generation thanks to the introduction of a new turbocharged V6 engine and energy recovery systems.
Sauber also had problems with their Ferrari-powered car on Saturday, with Adrian Sutil managing only one lap before stopping with smoke coming out of the power unit.
While the four Renault-powered teams have had more problems than others over the three pre-season tests, those using Mercedes units have been able to put in the mileage.
Germany's Nico Rosberg did 103 laps in the works Mercedes with his fastest time 0.226 seconds slower than Massa's one minute 33.258 seconds.
Ferrari's 2007 champion Kimi Raikkonen, who has replaced Massa, was third with 87 laps completed and Danish rookie Kevin Magnussen was fourth with 88 laps in the Mercedes-powered McLaren.
Germany's Nico Hulkenberg, whose Force India also has a Mercedes power unit, did 115 laps.
Renault-powered Toro Rosso and Caterham also had positive days, with the former's Russian rookie Daniil Kvyat doing 81 laps and the latter's Swedish newcomer Marcus Ericsson managing 117 - the most of any driver.
Ericsson ran nearly a full race simulation, including stops, in the morning before the session was halted by a red flag caused by another car stopping on track.
"The fact the car ran faultlessly all afternoon showed we'd pretty easily have finished a complete race mileage and that's very good news for the start of the season," said the 23-year-old Swede.
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