Lewis Hamilton led a McLaren one-two in practice for the first time this season, sparking hopes of a long-overdue victory for the team.
With both cars now sporting significant upgrades - Hamilton alone ran the new package in Germany 12 days ago - the silver machines were again back at the top of the timesheets in Hungary.
The reigning champion deposed long-time leader Kovalainen at the end of the session with his final hot lap, that after making errors on the previous two when he was gunning for a quick time.
Hamilton finished the day with a lap of one minute 22.079 seconds, just 0.047s ahead of Kovalainen, with Williams' Nico Rosberg third, a mere 0.075secs adrift, such was the close nature of the second session at the Hungaroring.
In fact, just 1.097secs separated the top 19 drivers, with rookie Jaime Alguersuari cast adrift at the bottom by 0.766secs to Toro Rosso team-mate Sebastien Buemi.
All the talk ahead of practice had surrounded Alguersuari, who on Sunday will become the youngest to compete in Formula One at the age of 19 years 126 days.
The likes of Jenson Button, Hamilton, Mark Webber and Felipe Massa had all commented yesterday on the youngster, suggesting he could destroy his career and that he was too young to be competing at this level.
Certainly, the first couple of laps were a little like watching Bambi on ice as Alguersuari tentatively made his way around the 2.7-mile track on the outskirts of Budapest.
But as he slowly became accustomed to the feel of a Formula One car, so he naturally improved, with his first timed lap 1:34.716, and finishing the day with a 1:23.942 after 82 laps overall.
Alguersuari far from disgraced himself during the two 90-minute sessions, finishing 1.950secs behind Kovalainen at the end of the first and 1.863secs off Hamilton after the second.
Expectedly defending the British F3 champion, Toro Rosso team boss Franz Tost said: "I hear some people say he is not experienced enough.
"It is always a difficult question to answer about when is a driver experienced enough to come into F1.
"I can only say Jaime has so far done 118 races, won 17 and been on the podium 46 times.
"He won last year's British Formula 3 championship, and this year in the World Series (by Renault) has been improving his performance race by race.
"I think he has a good background, and he is experienced enough to do a good job."
As a mark of respect, after competing with Henry Surtees in the British F3 championship last year, Alguersuari sported the words 'Ciao Henry' on the side of his helmet.
The dedication was in memory of the 18-year-old who was killed in a F2 race at Brands Hatch on Sunday.
Alguersuari still faces a considerable amount of work ahead of him, and it will probably take at least two or three grands prix before he is fully up to speed.
Completing the top five in practice were Red Bull's Webber and Sebastian Vettel sandwiching the second Williams of Kazuki Nakajima.
Rubens Barrichello was sixth for Brawn GP, with Button a surprising 13th, even though the heat of Hungary - with temperatures hitting 30 degrees - is supposedly more to the liking of the team's cars.
Ferrari duo Kimi Raikkonen and Massa were 11th and 18th, yet expect both to be strong in tomorrow's qualifying sessions.