The Dutch driver was top in both sessions, 0.768 seconds quicker than Mexican teammate and closest rival Sergio Perez (33) in the first and then 0.170 faster than Aston Martin's Alonso in the late afternoon.
"Overall I think we had a very good day, the car was in a good window," said Verstappen. "Short run and long run everything looked quite good."
Verstappen's fastest lap around Barcelona's Circuit de Catalunya was a one minute 13.907 second effort on soft tyres in practice two, with Alonso clocking 1:14.077.
The circuit has been shortened slightly, with the final chicane no longer used, and returned to a layout last used in 2006.
"It's been a lot more fun to drive," said Verstappen. "F1 cars in general feel better at high speed so for me the last two corners are much better to drive."
Alonso's 32nd and last win was at the same circuit a decade ago with Ferrari and his form at the age of 41 - with five podiums in six races including second in Monaco last weekend - has fired up the fans.
"It’s so close over one lap that I think a couple of tenths will put you in a completely different position in the classification, so we won’t read too much into the times," said the Spaniard.
"The fans have been amazing and it’s great to see their support. Hopefully we can put on a good show for them tomorrow."
FIRST WIN
Verstappen, who took his first F1 win at the circuit in 2016 and also won last year, leads closest rival Perez by 39 points after winning four of six races. Red Bull have won all six.
Alpine's Esteban Ocon (26), fresh from third place in Monaco last Sunday, was best of the rest in practice one while Haas's Nico Hulkenberg (35) was third in the second session with Perez fourth and Ocon fifth.
Ferrari introduced a new look upgraded car and Charles Leclerc (25) and Carlos Sainz (28) ended the day sixth and seventh.
Mercedes' George Russell (25), who had been trying out prototype Pirelli tyres for much of the first session, ended up eighth after being 10th in practice one, with seven-time world champion teammate Lewis Hamilton (38) 11th.
"I would say it was a difficult day one," said Hamilton, without showing much enthusiasm and leaving a lot unsaid. "I think just getting on top of the tyres and the deg (degradation). The car feels like a car.
"I think the long run pace didn't look terrible and we've just got to work and try and figure out how to extract more on a single lap.
"I think from the pace I had today it's a struggle for me currently to get into the top 10. But hopefully we'll do some changes overnight."
The top teams were all running with sensors and fluorescent 'flow-vis' paint in the first session as they sought aerodynamic data.
Several drivers also complained about the bumpy approach to the final corner, although Red Bull appeared to have got on top of the problem.
"It's not too bad. This track has been resurfaced a few years ago and it's still quite decent," said Verstappen.
