The two-time world champion took over at the front of the field with his first flying lap of the day, after Jean-Eric Vergne and Valtteri Bottas had led the way early on for day-one strugglers Toro Rosso and Williams.
Alonso spent the early part of his day working through short runs, often experimenting with cool-off laps in between faster efforts.
He was on course to improve his best time on a later run, but aborted the lap and headed for the pits.
Vergne and Bottas put in plenty of laps as their teams made up for hardly running on day one, completing 53 and 43 laps respectively by the halfway stage.
While most of the teams completed a decent amount of mileage, it was a surprise to see the first two red flags of the day caused by the until-now reliable Mercedes stopping on the circuit.
Reigning world champion Sebastian Vettel finally got a chance to run a few laps as Red Bull had its most productive morning of 2014 so far, but his total of 26 was made up of mainly short runs.
Red Bull mechanics were also ready with fire extinguishers when the car came into the pits, suggesting that the team is still cautious about temperatures at the rear of the RB10.
Other teams that did not feature much during the morning were McLaren and Lotus, with the latter working on solutions to get its engine running smoothly.
Kevin Magnussen took an early lunch while his team worked on the MP4-29, with the promise that the car would be back in action properly later in the day.
Caterham was unable to capitalise on its busy first day as Kamui Kobayashi took over from Robin Frijns, with the Japanese racer only completing eight laps at a reduced pace towards the end of the morning.