Italian Antonio Giovinazzi had been fastest for Alfa Romeo at lunchtime with a fastest lap of one minute 18.589 seconds but Norris, 19, put in a 1:17.709 in the afternoon sunshine on the soft C4 tyres.
The McLaren stopped twice on track, however, the first time due to an hydraulics issue.
Fernando Alonso, Spain's two times world champion who left McLaren and Formula One at the end of last year, was there to watch.
Canadian Lance Stroll went third for Racing Point on the fastest C5 tyres, ahead of Ferrari's Sebastian Vettel on harder C3 rubber.
Five times world champion Lewis Hamilton was the second slowest, just behind Mercedes team mate Valtteri Bottas, with only Renault's Nico Hulkenberg slower.
Bottas, who took over for the afternoon, did only one lap before an oil pressure problem stopped the car on track. The reigning champions then decided to swap out the power unit and he returned for six more.
Mercedes, focusing on heavier-fuel long runs, had a new front wing, nose and floor compared to those used last week and did plenty of aerodynamic testing.
Gasly did the most laps of any driver (136), and set his quickest lap on harder tyres than Norris, and team principal Christian Horner said it had been a very productive day at the Circuit de Catalunya.
"We've managed to get through our entire programme pretty much," he said. "It doesn't happen that often where everything you set out to do in the morning you have achieved by the afternoon.
"Honda are obviously doing a super job. We've been nothing but impressed at all levels with the product so far.
"There's still progress we need to make to catch the lead guys but it's certainly got off to a great start," he said of the new partnership with the Japanese manufacturer after years with Renault.
Williams had a more encouraging day, after missing most of the first test due to the late build of the car, with British rookie George Russell doing 119 laps.
The season starts in Australia on March 17.
(Writing by Alan Baldwin in London, editing by Alexander Smith and Toby Davis)
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