Team principal Christian Horner had forewarned their rivals on Thursday that, despite Vettel having already claimed his fourth successive drivers' title in India and with their fourth straight constructors' crown also in the bag, they would not let up and that proved to be the case at the Yas Marina circuit.
Vettel had finished third fastest in the first practice session but set the quickest time in the second, clocking up a time of one minute 41.335 seconds.
As soon as the majority of the field switched to run the soft compound tyre the Red Bull drivers flexed their muscles, with Webber topping the timesheets momentarily before ending the session 0.155secs adrift of Vettel.
Lotus' Romain Grosjean had outpaced the Red Bulls in the earlier session but his luck ran out when he suffered a brake disc failure shortly after switching on to the option tyre and he was down in 12th place.
The Frenchman's team-mate Kimi Raikkonen fared better as he clocked the fourth fastest time of the session, with the Mercedes of Lewis Hamilton a place ahead in third.
Nico Rosberg sat fifth at the end of the 90 minutes as Mercedes aim to open up a wider gap over Ferrari in the battle for second place in the constructors' championship.
Ferrari themselves were left struggling for pace, with Fernando Alonso eighth and Felipe Massa 10th after both had failed to break into the top 10 in the morning session.
McLaren seemed to have the beating of Ferrari on long stints and both Sergio Perez and Jenson Button set quicker times over one lap, ending the session sixth and seventh respectively with Button picking up a puncture.
The Saubers of Nico Hulkenberg and Esteban Gutierrez sandwiched Massa's 10th-placed Ferrari while Paul Di Resta also recovered from an early puncture to guide his Force India to 13th place.
Di Resta's team-mate Adrian Sutil was in 15th with the Williams of Pastor Maldonado splitting the Force India pair.
Daniel Ricciardo and Jean-Eric Verne could only guide the Torro Rossos to 16th and 17th with the second Williams of Valtteri Bottas 18th.
Caterham's Giedo van der Garde recovered from a spin to set the pace for the new teams with team-mate Charles Pic in 21st.
Jules Bianchi was 20th with Max Chilton, who also suffered a spin, sitting at the bottom of the timesheets for Marussia.