Kamui Kobayashi secured pole position for Toyota at the 24 Hours of Le Mans challenge in the first-ever Hyperpole shoot-out. Menezes took a surprise second position for Rebellion Racing in a tussle between him and the Japanese.
The American driver gave Toyota a scare as he beat Kobayashi’s then-provisional pole time 10 minutes into the new half-hour qualifying format with a time of 3:15.822s, but Kobayashi responded with a lap time of 3:15.267s to put him back on top.
"To be honest, a little bit disappointed because on my second attempt it seemed I could break my record," he said of his time.
"Unfortunately, I had the lap deleted (for exceeding track limits), so I had to stop. I was gaining already seven tenths, which is already breaking the record, so it’s a big shame."
Kobayashi has yet to win it, finishing runner-up in the last two years while compatriot Kazuki Nakajima stood on top of the podium with number eight car team mates Sebastien Buemi and Fernando Alonso.
The number eight Toyota, with Nakajima at the wheel, qualified only third this time with Rebellion Racing's number one R13 Gibson car splitting the two Japanese.
American Gustavo Menezes time in the Rebellion was a Le Mans record by a non-hybrid LMP1 car.
Rebellion's number three car qualified fourth.
In LMP2, former F1 driver Paul di Resta, driving for United Autosport, broke the lap record with an impressive 3:24.528s.
Menezes ensured Rebellion Racing were top of the timesheets in Friday morning’s fourth practice session.
He posted a time of 3:21.132 going into the final quarter of the 60-minute session and was half a second quicker than Mike Conway in the second-placed No. 7 Toyota TS050 Hybrid.
Louis Deletraz ensured the other Rebellion R13 Gibson came third with a time of 3:22.328s.
Rebellion Racing and Louis Deletraz tops Le Mans after FP3 which featured four hours of night running.
Deletraz went top of the timesheets in the first hour of the night session with a 3:19.158s lap in the #3 Rebellion R-13.
Toyota's Kamui Kobayashi, in the #7 Toyota TS050 Hybrid, set a time of 3:19.638s (+0.480s) in the second hour with the second Rebellion driver Gustavo Menezes (+0.617s) taking third.
The session had to be finished 15 minutes early after a huge accident involving Brit Bonamy Grimes in the Red River Ferrari. He smashed into the barriers at the Mulsanne chicane and was fortunate to come out of it unharmed.
In LMP2 Tristan Gommendy set the fastest time early on with 3:28.013s in the #30 Duqueine ORECA 07.
Toyota Gazoo Racing and Rebellion both claimed two spots for Friday's Le Mans 2020 Hyperpole. Toyota grabbed the first two places with times of 3:17.089 and 3:17.336.
Behind them came Rebellion racing in third and fifth, in 3:21.598 and 3:24.632, bookending Bykolles in 3:24.468.
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LMP2 meanwhile produced a much tighter set of results. Racing Team Nederland recorded a time of 3:26.48, and Jackie Chan DC, G-Driveand High Class all took a place.
United Autospots claimed two spots to complete the challengers for Friday.
Additional reporting from Reuters.