The Briton, who switched from Carlin to DAMS for a shot at this year's title, worked his way down to a 1m49.126s in the final hour of the day.
That left him just one tenth of a second clear of Mitch Evans, who will drive for 2013 teams' champions Russian Time this season.
Palmer's team-mate Stephane Richelmi finished half a second down the road, in third overall.
Palmer joins DAMS for 2014 title shot
Daniel Abt, driving for Force India junior team Hilmer, wound up fourth, just ahead of Formula Renault 3.5 convert and McLaren protege Stoffel Vandoorne.
GP2 race winners Johnny Cecotto and Stefano Coletti sandwiched Felipe Nasr in the fight for sixth, with Coletti the last man to break the 1m50s barrier on day one.
Rio Haryanto led Caterham stable-mate Alexander Rossi in the morning session, but the pair both dropped down the order as conditions improved in the afternoon.
Rossi wound up ninth overall, while Haryanto was 13th, fractions ahead of last year's European Formula 3 champion Raffaele Marciello.
Four red flags - for Artem Markelov, Facu Regalia, Julian Leal and Axcil Jefferies - punctured the day.
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