Inside the first three minutes, Drogba latched on to a long clearance by Petr Cech and used his strength to hold off and turn Ben Turner before sending a low shot wide of the far post.
Drogba's industry soon brought him a reward, although his goal owed as much to some terrible defending from the home side as it did his own good work.
Dann failed to clear after a poor header by Turner and Drogba shrugged him aside before rounding goalkeeper Kieran Westwood and smashing the ball high into the net.
Coventry responded well, especially when Leon Best and Freddy Eastwood ran at the visitors, but they failed to test Cech and Chelsea were also continuing to look dangerous.
Hiddink's tactics, with Florent Malouda and Salomon Kalou operating on either side of Drogba, often had Coventry at full stretch and Michael Ballack was unlucky to see his shot blocked after Frank Lampard and Jose Boswinga had carved the home defence apart.
Lampard, who was orchestrating many of Chelsea's attacks from the middle of the park, almost added a second goal himself with a dipping 30-yard free-kick before half-time that Westwood did well to tip over.
And, while the hosts continued to press in the second period, their failure to create a meaningful chance meant they looked no nearer to finding an equaliser.
The home side's best moments came when their long-throw expert Aron Gunnarsson launched the ball into the Chelsea penalty area.
But one of those set-pieces led directly to Chelsea's second goal when Hiddink's side broke quickly and Quaresma's searching ball was easily converted by the unmarked Alex.
It was a satisfying day for Hiddink, who maintained his 100% winning record as Blues boss and was also able to bring Michael Essien off the bench in the second half for his first appearance after over six months out with a knee ligament injury.
Hiddink's starting line-up had included defender Ashley Cole, who received an £80 fixed penalty fine for being drunk and disorderly in the early hours of Thursday morning.
Coventry City boss Chris Coleman: "This was the biggest game for the club at this new stadium, but we need to move on.
"It is going to be difficult against Bristol City [In the Championship] on Tuesday, but we've got to get back on it. We will have to get back to reality."
Chelsea manager Guus Hiddink: "Didier is dangerous. He is working very hard and he is good for the team.
"There are still some little things that he needs to improve on, but he is working on them in sessions outside of training which he likes."
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