Drogba scored the goal which extended the Blues' unbeaten home record in the Premier League to 69 matches as Everton grabbed a deserved point at Stamford Bridge.
The Ivorian struck on 71 minutes, but Everton's defensive display reaped dividends with seconds remaining when Cahill equalised with an acrobatic effort.
It was the Toffees who had the first chance on goal on 15 minutes when Ayegbeni Yakubu put a deep right-wing cross into the path of Steven Pienaar, but the midfielder completely mis-timed the flight of the ball when he was free in the six-yard box.
Ricardo Carvalho suffered a back injury on 22 minutes after a challenge with Yakubu and, after returning to the pitch, limped around in midfield.
Frank Lampard had Chelsea's first effort on goal when Nuno Valente headed his trademark drive from just outside the Everton area off the line on 26 minutes.
Chelsea boss Avram Grant eventually replaced the hapless Carvalho on 28 minutes with Tal Ben Haim.
Everton had another let off when Drogba and Lampard set up Joe Cole but he couldn't get a shot away, before Tim Howard produced a fantastic one-handed save to deny another Lampard piledriver.
Drogba missed an open goal on 45 minutes when a quick break by Wayne Bridge found Shaun Wright-Phillips.
The wideman sent in a low ball across goal, but Drogba, like Pienaar earlier, completed mis-timed the ball with an open goal going begging.
Everton boss David Moyes must have fancied his chances of winning the game as he brought on two strikers as half-time with Victor Anichebe on for Yakubu and James McFadden replacing Phil Neville.
Grant was forced into bringing on Salomon Kalou on 64 minutes for Wright-Phillips.
Chelsea almost scored twice within seconds soon after when first Howard tipped away a deft Lampard chip before right-back Tony Hibbett scrambled the ball off the line after a left-foot drive from Alex.
Chelsea finally broke the deadlock with 19 minutes remaining when a corner from Kalou was met by Drogba at the near post and the Ivory Coast hitman glanced a powerful header past Howard.
It is Drogba's seventh goal for the Blues this season.
Drogba almost hit number two when he went on a long, mazy run but finished the move off with a limp shot which Howard grabbed gleefully.
But Everton deserved their point and it came with a minute to play when McFadden's shot on target was deflected into the air and Cahill produced an overhead kick from six yards out that beat the stranded Carlo Cudicini.