The Briton's morning ground to a halt after just three exploratory laps due to a fuel-pump failure on his McLaren, and he remained sidelined until the midway point.
A similar problem led to Lewis Hamilton's retirement from the lead of last year's Abu Dhabi Grand Prix.
Button was eventually able to resume and in the final minutes of the session clocked a 1m18.861s on Pirelli's new hard compound tyres, putting him more than eight tenths clear of the field.
Second was claimed by Mark Webber, after the Australian staged his own late rally following a modest morning in the title-defending Red Bull RB9.
Webber jumped ahead of Romain Grosjean's Lotus with a 1m19.709s, only for Button to trump that almost immediately.
That left morning pacesetter Grosjean in third, Force India's Paul di Resta fourth and Toro Rosso's Daniel Ricciardo fifth, the trio all having set the fastest times in the morning.
Di Resta clocked up more laps than any other driver, his final tally standing at 89.
Felipe Massa managed to improve in the Ferrari F138 and ended the day sixth fastest, albeit 1.6s down on Button.
On his first day testing for Sauber, Nico Hulkenberg was seventh fastest, just ahead of Nico Rosberg and the stricken Mercedes camp.
Rosberg had been setting the pace in the morning but his run - and his day - came to a premature end due to an electrical fault.
Mercedes eventually had to abandon the rest of the day as it waits for new parts. Hamilton is set to test for the first time tomorrow.
Pastor Maldonado, driving the old-spec FW34 Williams, finished just ahead of F1 rookies Giedo van der Garde and Max Chilton.
Chilton went off at Dry Sac shortly after setting his fastest time in the afternoon, with Marussia later identifying a fault with the rear suspension.
1. Jenson Button McLaren 1m18.861s 37
2. Mark Webber Red Bull 1m19.709s + 0.848s 73
3. Romain Grosjean Lotus 1m19.796s + 0.935s 54
4. Paul di Resta Force India 1m20.343s + 1.482s 89
5. Daniel Ricciardo Toro Rosso 1m20.401s + 1.540s 70
6. Felipe Massa Ferrari 1m20.536s + 1.675s 64
7. Nico Hulkenberg Sauber 1m20.699s + 1.838s 79
8. Nico Rosberg Mercedes 1m20.846s + 1.985s 11
9. Pastor Maldonado Williams 1m20.864s + 2.003s 84
10. Giedo van der Garde Caterham 1m21.915s + 3.054s 64
11. Max Chilton Marussia 1m24.176s + 5.315s 29