Piastri saw off team-mate Lando Norris as McLaren secured a front-row lockout.
Lewis Hamilton was knocked out of Q2 and qualified only 12th in his Mercedes for the 19-lap dash, which gets under way at 8:30pm local time (6:30pm BST).
Verstappen will wrap up his third consecutive title if he finishes sixth or better, or if Red Bull team-mate Sergio Perez fails to finish inside the top three in the sprint at the Lusail International Circuit. Perez qualified only eighth on yet another scruffy outing for the struggling Mexican.
A day after taking top spot for the start of Sunday’s 57-lap main event, Verstappen, who has dominated all year, saw his first lap in Q3 deleted for exceeding track limits at Turn 5.
And the 26-year-old Dutchman was unable to do enough on his final run to usurp Piastri, finishing two tenths behind the rookie Australian.
Norris was in the running for first place but he ran wide at the last corner and failed to improve on his earlier effort.
George Russell finished fourth for Mercedes – four tenths behind Piastri – and ahead of Carlos Sainz and Charles Leclerc, who took fifth and sixth respectively for Ferrari.
Sprint qualifying at a windswept Lusail – 18 miles north of Doha – was delayed amid fears over the safety of the tyres.
The running had been due to start at 4pm local time (2pm BST), but was delayed by 20 minutes following revisions to the track limits.
The drivers took part in an additional 10 minutes of practice to familiarise themselves with the changes made to the track at turns 12 and 13 prior to qualifying.
Formula One’s governing body, the FIA, said “a separation in the sidewall between the topping compound and the carcass cords” were discovered on the Pirelli tyres following yesterday’s one-hour running.
The federation believe the problem is likely to have been caused by a number of the high kerbs used at the circuit.
An emergency summit was staged in the build-up to qualifying with the drivers assured they would not be put in harm’s way.
Additional analysis will take place following today’s sprint race and further action – which will include three mandatory tyre stops – may be taken for Sunday’s grand prix.
Lance Stroll shoved his British performance coach and stormed out of a television interview after he was eliminated from Q1 in Friday’s running.
And the under-pressure Canadian fell at the first hurdle again on Saturday, one place better off in 16th.
Stroll’s Aston Martin team-mate Fernando Alonso, who also saw his best effort in qualifying chalked off for exceeding track limits, lines up in ninth.
Qatar Sprint Shootout Times:
1 Oscar PIASTRI McLaren 1:24.454
2 Lando NORRIS McLaren +0.082
3 Max VERSTAPPEN Red Bull Racing +0.192
4 George RUSSELL Mercedes +0.387
5 Fernando ALONSO Aston Martin +0.505
6 Carlos SAINZ Ferrari +0.701
7 Charles LECLERC Ferrari +0.793
8 Nico HULKENBERG Haas F1 Team +0.866
9 Sergio PEREZ Red Bull Racing +0.928
10 Esteban OCON Alpine no time
11 Pierre GASLY Alpine 1:25.686
12 Lewis HAMILTON Mercedes 1:25.962
13 Valtteri BOTTAS Alfa Romeo 1:26.236
14 Liam LAWSON AlphaTauri 1:26.584
15 Guanyu ZHOU Alfa Romeo 1:54.546
16 Lance STROLL Aston Martin 1:26.846
17 Alexander ALBON Williams 1:26.862
18 Yuki TSUNODA AlphaTauri 1:26.926
19 Kevin MAGNUSSEN Haas F1 Team 1:27.438
20 Logan SARGEANT William 2:05.741
