Spurs looked a shoo-in for Champions League qualification just over three weeks ago, with Harry Redknapp's third-placed side on course to move 10 points clear of the Blues just before half-time of last month's north London derby.
But a spectacular reversal of fortunes since means that, come Saturday afternoon, Chelsea could leapfrog Tottenham and become firm favourites to finish best of the rest behind the Manchester clubs.
To do so, they must better Spurs' result on Wednesday night when the two sides play Manchester City and Stoke, respectively, before beating Redknapp's men in Saturday's derby showdown at Stamford Bridge.
On current form, you would not bet against the latter result, while history shows Chelsea have qualified for the Champions League every season since 2003, with Tottenham having done so just once.
Asked if that gave his fifth-placed side the advantage, Blues goalkeeper Cech said: "I think, yes. We have been together through so many situations in eight years and a lot of people here remember those, so we have the benefit of the experience of that.
"We seem to cope with the difficult situations quite well so, hopefully, this experience we've got throughout the years will help us reach our targets.
"We are approaching these next two games with confidence now."
Things could have hardly gone more Chelsea's way since they sacked manager Andre Villas-Boas just over two weeks ago.
Four successive victories have catapulted them into the Champions League quarter-finals and FA Cup semi-finals, while keeping them in the top-four hunt.
They are suddenly injury-free and Fernando Torres has finally found his shooting boots after breaking his agonising goal drought against Leicester on Sunday.
Cech said: "We know that this could be a fantastic two weeks of the season for us - last week and this week.
"We have already qualified for the quarter-finals of the Champions League, we're now in the semi-finals of the FA Cup and, after these two League games, we could be third."
Caretaker boss Roberto Di Matteo must take much of the credit for giving Blues fans hope of a fairytale finish to the season.
Cech said: "He understood quickly what he had in the team.
"He is a Chelsea legend and you can see the reception he gets around here - it makes a difference. The atmosphere at the stadium is a lot more positive.
"When you get results, the mood around the camp changes."
Cech revealed it only took one win to spark the turnaround.
"The important one was the first one when we won the replay against Birmingham," he said.
"That gave us confidence and got us through to the next round of the FA Cup.
"We followed it up by beating Stoke and we had two consecutive clean sheets.
"It gave us more confidence and obviously we wanted to show that we could play better than we were doing before.
"You can see everybody is trying to change things around and, suddenly, we're getting a bit of luck as well."
Torres can testify to that, having ended 25 hours and 41 minutes without scoring.
Cech said: "He must be delighted because, as a striker, you want to score goals and this will be great for his confidence.
"We need him because we have some massive games coming up and it will be great if he can score."
Cech also took time to reflect on the events at White Hart Lane on Saturday that left Bolton midfielder Fabrice Muamba fighting for his life.
Muamba, who suffered a cardiac arrest, benefited from the changes to medical procedures that were implemented after Cech fractured his skull during a match five and a half years ago.
"I was watching the game," Cech said.
"I was looking for the news all the time.
"I knew we had an important game the next day but the life of a person is more important than football.
"Our thoughts are with his friends and family."