The Toffees' third victory of their Group A campaign put them into the hat for the last 32 with one match - away at AZ Alkmaar later this month - still to play.
Mikel Arteta's first-half penalty miss looked like being costly as ten-man Zenit appeared to have done enough to earn a point.
But Cahill popped up five minutes from time to scramble the ball home after Joleon Lescott's close-range drive was only parried by goalkeeper Viacheslav Malafeev.
The newly-crowned Russian champions had survived the harsh first-half dismissal of Nicolas Lombaerts before that cruel blow.
Lombaerts was dismissed in a sometimes tempestuous affair at Goodison Park after the referee ruled he blocked Cahill's goalbound shot with his hand despite it clearly appearing to strike his chest.
However, justice appeared to have been done when Arteta drilled the 29th minute spot-kick over the crossbar.
Everton boss David Moyes made changes to his line-up ahead of a busy December programme both on the domestic and European front.
James McFadden and Leighton Baines were drafted into the line-up, while Leon Osman and Ayegbeni Yakubu were dropped to the bench.
However, it was the Toffees' industrious midfield unit which caused most of the first-half problems as Arteta saw a third minute effort acrobatically cleared off the line by Dong-Jin Kim.
The Spanish playmaker then saw a superb 30-yard free-kick destined for the top corner tipped away by the impressive Malafeev.
Two minuets later, Lee Carsley placed a left-foot shot onto the inside of the upright with the keeper beaten as the home side made the most of their man advantage.
But the visitors always looked dangerous on the break and created a string of chances orchestrated by the dangerous Andrei Arshavin.
Pavel Pogrebnyak drew a fine save from the advancing Tim Howard after being put through by Arshavin in the 50th minute and soon after Konstantin Zyrianov fired over the crossbar when well placed just inside the penalty area.
Steven Pienaar and Arteta had shots that flashed wide midway through the second half as both sides continued to play open and attacking football.
But with a draw on the cards, Cahill was in the right place at the right time to stab home the winner after Lescott's flick from a corner was returned to him and he dispatched a low drive which the keeper could only palm into his path.