Charles Leclerc was third for Ferrari’s first podium of the campaign and Norris clawed his way from 10th on the grid to fourth.
He now leads Norris, whose race was heavily compromised by a crash in qualifying, by 10 points after starting the night three behind.
George Russell was fifth for Mercedes with Italian teammate Kimi Antonelli sixth and seven-times world champion Lewis Hamilton seventh for Ferrari.
Williams had Carlos Sainz and Alex Albon eighth and ninth, with Racing Bulls’ French rookie Isack Hadjar the final points scorer in 10th.
Stewards decided the champion was at fault and handed him the penalty, with Verstappen reacting by saying sarcastically, “Oh, that is lovely.”
The safety car continued a sequence of appearing at all five races in Saudi Arabia so far, with an appearance at the end of the opening lap after Verstappen’s teammate Yuki Tsunoda and Alpine’s Pierre Gasly collided and crashed.
Both drivers retired, Tsunoda after getting his car back to the pits.