Oscar Piastri endured a disastrous weekend in Baku, crashing out of the race after jumping the start and stalling, which ended his 34-race finishing streak.
Norris attributed his performance to a poor qualifying session and his McLaren's lack of pace, stating he felt he maximised his race despite the struggles.
Norris suffered another slow pit stop and rejoined eighth, where he was eventually able to overtake Charles Leclerc for seventh place.
Max Verstappen secured a dominant lights-to-flag victory, George Russell achieved second place despite battling illness, while Carlos Sainz delivered Williams' first podium since 2021.