The England midfielder pounced in the 69th minute to ensure a 3-1 aggregate semifinal victory, and a Feb. 24 meeting with three-time winner Tottenham at Wembley. This competition isn't a major competition," Chelsea manager Avram Grant said. "But any game we can win, any trophy we can take, we will do everything it takes."Wednesday's clash at Goodison Park couldn't match the drama produced by Spurs, who beat Arsenal 5-1 in the other semifinal a day earlier.
The African Cup of Nations left Grant without Salomon Kalou, Michael Essien, Didier Drogba and John Obi Mikel. Injuries ruled out midfielders Frank Lampard and Michael Ballack, while captain John Terry and striker Andriy Shevchenko also didn't make the trip to Liverpool.
"It's not easy because even when we had all the players and all the squad most people said we would not succeed so much," Grant said.
"It's a big test of character and the players are doing a great job. Now you see have a good squad. It's not easy to find good players, because these players belong to Chelsea are quality players and have good character."
Shaun Wright-Phillips started despite an ankle injury from the weekend and was denied a third-minute goal when Joleon Lescott deflected his close range effort wide.
Lescott, whose late own-goal at Stamford Bridge two weeks ago gave Chelsea a 2-1 first-leg win, tried to used his aerial presence to rally Everton. In the ninth minute, he headed Mikel Arteta's corner goalward only to be denied by Petr Cech.
The Toffees dictated play early, but couldn't create another threatening move until the 19th minute when Andy Johnson struck wide.
Nicolas Anelka, making his second start with Chelsea since moving from Bolton, struggled to make an impact as he was repeatedly caught offside and his first shot in the 29th minute didn't trouble Tim Howard.
Determined to snap an 18-match winless streak against Chelsea, Everton was the sharper side after the break, tenaciously pressurizing Cech.
But the Chelsea keeper twice thwarted Everton forays in the first 15 minutes, first denying captain Phil Neville and then blocking a backheel from Phil Jagielka.
"I think we played well in periods of the game," Everton manager David Moyes said. "It was a brilliant effort from the players, but we need to find that bit extra that gets you to cup finals or gets you into the top four.
"We need to find the magic ingredient if we can."
Chelsea capitalized on Everton's missed opportunities, exploiting the wings on a counter for its only goal.
Florent Malouda dispatched a deep, diagonal pass from the half way line to Cole, and the England midfielder settled the ball before beating Howard.
"We needed it, we were under a lot of pressure," Cole said. "We stick together from back to front. Everyone defends and attacks together."
With the Toffees needing to score twice to force extra time, Cech beat back any hopes of an Everton rally, palming over Johnson's fierce shot from close ranger two minutes later.
The loss extended Everton's cup frustration against the Blues, not having beaten the Blues since February 1956 in the FA Cup.
"We've been on the end of a few bad semifinal experiences in Liverpool but it will be a nice flight home tonight," said Cole, referring to Champions League defeats against Liverpool in 2005 and 2007.