Carlo Ancelotti's men made a mockery of their poor pre-season – the previous weekend's 3-1 Community Shield defeat to Manchester United at Wembley was their fourth successive loss – as the newly-promoted Baggies were ripped apart by clinical finishing.
Drogba netted a hat-trick while Florent Malouda added a brace and Frank Lampard also opened his account.
The Blues certainly laid down a marker of intent to continue where they finished off in last season's drive towards the title, which saw Chelsea win successive home games 7-0 and 8-0.
Drogba, though, is under no illusions that plenty of tougher tests lie ahead if Ancelotti's men are to remain the team to beat.
"It is important for us to keep playing the way we did last year, but also trying to improve because it is going to be harder," the 32-year-old said.
"We are champions and this season is going to be really difficult. All of the other teams are improving in terms of bringing in new players. However, our team is really hungry.
"We may have not signed a lot of players, but we still have quality players and now we have Yossi (Benayoun) and Ramires too."
West Brom manager Roberto di Matteo's return to Stamford Bridge had a not entirely unexpected outcome.
The Baggies, promoted as runners-up in the Championship last season, did at least try to stick to their passing principles, but tellingly lacked quality in the final third.