This game had been billed as a friendly, but it was nothing of the sort as these two heavyweights sought to achieve a mental advantage ahead of the start of the new Premiership season next week.
Ivory Coast striker Drogba, who had an indifferent debut season at Stamford Bridge, showed why Jose Mourinho holds him in such high regard.
Within nine minutes of the start, and with Arsenal camped in Chelsea's half, a deep left-wing cross by Asier del Horno was collected by Drogba on his chest, on the edge of the penalty area.
With Philippe Senderos behind him, Drogba cut past the centre-back and arrowed into the penalty area. He still had work to do, but found space between the Swiss defender and Jens Lehmann.
In one swift movement, Drogba flashed an excellent left-footer across Lehmann's path and into the far right-hand corner of the net.
Arsenal, to their credit, did not panic and their assured play meant they had plenty of time to get back into the game.
They almost equalised straight away but Thierry Henry's clipped shot on the edge of the box produced a fine save from Petr Cech.
However, Chelsea increased their lead in the 56th minute. A quick counter-attack by the Blues began in midfield when Eidur Gudjohnsen headed on and Drogba latched onto the ball and attacked the penalty area.
He first had to hold off a robust tackle by the ponderous Senderos before shielding the ball from the advancing Lehmann. Drogba then turned and clipped the ball into the net from eight yards out.
Arsenal made six substitutions in all and got their reward in the 65th minute when Cesc Fabregas latched onto a low byline cross to steer the ball from eight yards out past Cech's right-hand dive and into the net.
Arsenal upped the pace towards the end but Chelsea shut up shop and ran out worthy winners.