Norris bounces back to top final Baku practice
The 24-year-old Briton, 10th after damaging his car in the second practice, clocked an impressive best lap in 1min 41.223sec in difficult windy conditions on the unforgiving Baku street track.
Norris' lap lifted him 0.222 seconds clear of reigning world champion Verstappen and Piastri.
Piastri leads Norris by 31 points in the drivers' title race and they could clinch McLaren's second consecutive constructors' title on Sunday.
After topping the times on Friday, seven-time champion Lewis Hamilton was fourth for Ferrari ahead of much-improved rookie Kimi Antonelli and his Mercedes team-mate George Russell, Williams’ Alex Albon and rookie Oliver Bearman of Haas.
Racing Bulls' rookie Liam Lawson was ninth ahead of Charles Leclerc in the second Ferrari after an hour of unpredictable but highly-competitive action.
Lawson was first out on a leaf-strewn track ahead of Bearman, five minutes into the session, and immediately noted the wind.
"It's just sketchy everywhere, every corner feels worse," complained Norris after joining the fray.
A clutch of drivers clocked best laps, but without matching Friday's pace before Hamilton went top, soon followed by Piastri and then Leclerc in 1:42.354.
Leclerc, seeking a fifth consecutive pole and a first win in Baku, trimmed his time, but it was not enough to resist a storming lap from Verstappen whose 1:41.727 lifted him six-tenths clear.
Norris then went top with 10 minutes remaining in 1:41.223 after Albon went third.
In a furious finale, Hamilton took on a new set of tyres and rose from 12th to third, two-tenths off the pace.
In a fiercely competitive session and tricky conditions, the top ten were separated by less than a second and Leclerc finished down in 10th.