McLaren's Lando Norris had set the pace in first practice, 0.024 quicker than Red Bull's triple Formula One world champion Max Verstappen, and the Briton was third in the second FP2 session.
Verstappen dropped to fifth in that session, albeit on slower medium tyres compared to others on softs, with Alpine's Pierre Gasly a surprisingly fast fourth and Ferrari's Charles Leclerc sixth.
Seven times world champion Hamilton set a best time of one minute 13.264 seconds, 0.022 quicker than Sainz, after Norris had led FP1 with a lap of 1:14.228.
Sainz was third on those first practice timesheets as Formula One prepares for a triple-header of races on successive weekends.
Verstappen's teammate Sergio Perez, who will have a three-place grid penalty on Sunday carried over from Canada, was fifth and 13th respectively.
Mercedes's George Russell was eighth in session two, just behind McLaren's Oscar Piastri.
The lap times compared to last year's first free practice best of 1:14.606, when the then-dominant Red Bulls were one-two and Verstappen a mighty 0.768 quicker than Perez, and Verstappen's 1:13.907 in 2023's second session.
The battle at the top has got a lot closer since then and there were five teams in the top five in Friday's second session after four in the top four earlier in the day.
The gap between Hamilton and Sauber's Valtteri Bottas in 10th place in second practice was 0.660, while only 0.683 separated Norris and seventh-placed Hamilton in the first.
"All in all a good start to the weekend...I'm sure it's going to be close again, like it was in Canada," said Norris, looking forward to Saturday's qualifying.
Three teams and four drivers have won already this season and Verstappen, chasing his third Spanish GP win in a row, faces more of a battle despite leading Leclerc by 56 points in the drivers' standings.
"I think you have four teams that are on top of each other and as always it will be about execution," McLaren boss Zak Brown told Sky Sports.
"Everyone knows this track. We test here a lot, so this weekend will show us how things might look like for the rest of the year."
While McLaren have no significant upgrades on their car, Ferrari have brought seven new items including changes to the floor and diffuser.
Britain's Oliver Bearman, tipped for a race seat next season, replaced Nico Hulkenberg at Haas for the first session and completed 29 laps to end up 19th compared to Kevin Magnussen in 17th.
That session was briefly halted with 22 minutes to go when Alonso's car shed part of his front wing at turn nine.
Russell and RB's Yuki Tsunoda also had a near miss, with the Japanese almost hitting the rear of the Mercedes.
"Don't know what Tsunoda was doing there," Russell said over the radio. "I pulled to the right and he just aimed for me."
