Lewis Hamilton will start the inaugural race at the Losail International Circuit from pole position, his first in nine races and the 102nd of his F1 career.
But he will be joined on the front row by AlphaTauri's Pierre Gasly whose puncture in the final moments of qualifying sparked investigations into Verstappen and Bottas.
Red Bull driver and championship leader Verstappen drops five places from second to seventh after being found guilty of ignoring double-waved yellow flags as Gasly's stricken car crawled slowly onto the main straight.
Bottas has been handed a three-place penalty for not seeing single-yellow flags and drops to sixth from third.
As Bottas completed his timed lap first, his penalty was also applied before Verstappen's.
Ferrari's Carlos Sainz has avoided a penalty for an alleged single yellow-flag breach and will start fifth.
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