With storm clouds overhead the drivers raced out early to take advantage of the track while it was still dry.
Button was the first man to put a lap in on the super-soft tyres, setting a mark of a minute 15.746 seconds that was certain of being the best time of the day after the rain set in approximately 15 minutes into the session.
Romain Grosjean of Lotus, using the soft compound tyres, was four-tenths of a second back in second place, with the Ferrari duo of Felipe Massa and Fernando Alonso third and fourth respectively, and Pastor Maldonado in the Williams finishing fifth.
Lewis Hamilton was down in 11th, a place below defending world champion Sebastian Vettel, but with the rain playing such a prominent part in the session, the placings were scarcely a reflection of most teams' and drivers' true pace.
It will mean that the final 60-minute session before qualifying on Saturday morning will be a hectic one, with plenty of set-up work for the teams still left to tackle.
As the start of the testing window was signalled, it looked as if Monaco was set for a deluge - but in the event the rain was light and persistent.
After a flurry of early activity the rain duly set in, and most drivers opted to wait patiently in the garage.
The Toro Rosso duo of Jean-Eric Vergne and Daniel Ricciardo ran virtually on their own for some time on intermediate tyres, setting lap times around 20 seconds down on Button's earlier mark in the dry.
The slippery track was a key problem, with five men including Felipe Massa and both Williams drivers running off at turn six into the Mirabeau, several drivers missing the chicane at the end of the tunnel, and turn 14 reported as particularly treacherous.
As conditions improved towards the end of the session most drivers ventured out, but nobody risked switching back to slick tyres.
The forecast for the rest of the weekend in Monaco is mixed, and at a unique track where set-up matters, most teams will feel they did not get a great deal out of a tricky session.