Lewis Hamilton had led Jenson Button from the early part of the day but the Finn took over with three minutes remaining of the second session.
Appreciably, conditions for the second 90-minute period were markedly different to those in the first as outgoing champion Hamilton pipped new title-holder Button by just 0.096 seconds.
Earlier in the day, as the drivers acclimatised themselves to the new Yas Marina circuit, they basked in temperatures of 35 degrees Celsius.
It was still 31 degrees when the second session began at 5pm local time, but on this occasion the following 90 minutes would be played out under a setting sun for the first time in F1 history, and ultimately floodlights as day shifted into night.
That is when the splendour of the circuit came into its own as the cars sped past the marina with all the yachts lit up, and moreover, the five-star Yas Hotel that straddles the circuit.
Prior to Abu Dhabi's day of reckoning, it was Kovalainen who led the way with a time of one minute 41.307secs, over 2.5secs quicker than Hamilton's best earlier in the day.
But that was no surprise as the 20 drivers grew accustomed to the track, culminating in the Finn ending up quicker than his McLaren team-mate by 0.197secs, with Brawn GP's Button 0.234secs down on Kovalainen.
Sebastian Vettel, looking for a small degree of consolation for the year by finishing second to Button in the championship, was fourth quickest in his Red Bull, 0.284secs behind Kovalainen.
Toyota's Kamui Kobayashi, who is fast proving himself in F1 as he again deputises for the injured Timo Glock, was fifth, followed by Toro Rosso's Sebastien Buemi and Red Bull's Mark Webber, winner in Brazil last time out.
The top 10 was completed by Brawn's Rubens Barrichello, who himself has designs on finishing runner-up to his team-mate, with Williams' Nico Rosberg ninth and Kimi Raikkonen in his Ferrari 10th.
BMW Sauber's Robert Kubica finished bottom of the timesheets, but that after blowing an engine after 13 laps.
That will likely incur a 10-place grid penalty for the race as he has already used the permissible eight engines for the season.
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