Essien, recently back from a long layoff with a knee injury, beat City keeper Shay Given in the 18th minute to seal the victory that left Chelsea four points behind leaders Manchester United who lost 4-1 at home to Liverpool on Saturday.
Champions United, who have played a game fewer than their rivals, have 65 points with Chelsea and Liverpool on 61.
Aston Villa's poor run continued in a 2-1 home defeat by Tottenham Hotspur which left them below fourth-placed Arsenal in the race for a Champions League spot.
Since Dutchman Hiddink replaced Luiz Felipe Scolari, Chelsea have gone seven matches unbeaten and after United's defeat on Saturday are still in the title race.
Hiddink has also steered them into the FA Cup semi-finals and the last eight of the Champions League.
The only worries for Hiddink were that Chelsea failed to turn their dominance into more goals and that midfielder Deco and striker Didier Drogba hobbled off.
"We were happy with the win but if we had got the second goal we could have won three or four nil," Hiddink told the BBC.
"We were not anxious because defensively we were OK but nevertheless we should have killed off the game."
HAMSTRING INJURY
Hiddink said Drogba's injury was not serious but that Deco could be out for the season with a hamstring injury.
Big-spending City, who have won just once away in the league this season and are still not clear of relegation worries, were poor and could have been behind even before Ghana international Essien diverted in Frank Lampard's shot with his shin.
Former City player Nicolas Anelka had a strong penalty appeal turned down shortly before halftime and Juliano Belletti fired a low drive against the post after the break.
Michael Ballack also wasted a good chance and Florent Malouda, who replaced Drogba, should have scored as the game drifted to a predictable conclusion.
Villa had the chance to move back into fourth spot against a Spurs side still looking for points to stay away from relegation trouble.
However, they fell behind to an early Jermaine Jenas goal and Darren Bent tapped in a second for Spurs after the break. Striker John Carew pulled a late goal back for Villa but they slipped to a third defeat in four league games.
Tottenham moved up to 11th, six points above Stoke City who are third from bottom.
CHELSEA FANS! Check FourFourTwo.com’s ever-expandinginterviews archivefor more stuff to read:
