Kobayashi took the top spot with a best time of 1m27.794s around halfway through the 15-minute Hypercar qualifying session on Saturday afternoon, scoring a crucial bonus point for himself and his team-mates Jose Maria Lopez and Mike Conway.
Brendon Hartley was 0.624 seconds adrift of Kobayashi in the #8 Toyota, ahead of the two factory Penske-run Porsche 963s.
Kevin Estre briefly topped the times at the wheel of the #6 Porsche before both Toyotas set their fastest times of a session that took place on a virtually dry track, but with some damp patches from earlier rain.
The French driver's effort of 1m28.687s was still enough for third ahead of team-mate Frederic Makowiecki in the sister #5 car.
Next up was the solo Cadillac V-Series.R driven by Alex Lynn, who was the last driver to get within a second of the pace of Kobayashi.
Ferrari suffered a subdued qualifying session as its pair of 499Ps could only manage sixth and seventh places, marking the first time this season it hasn't got one of its cars in the top three.
James Calado set the Italian marque's best time of 1m28.991s, almost 1.2s off the pace, in the #51 car, while Nicklas Nielsen was fractionally slower in the #50 Ferrari.
Source: Autosport