The Blues beat Birmingham 3-1 to climb above Arsene Wenger's side on goal difference after the Gunners threw away a 3-1 lead and drew 3-3 at Tottenham.
Both sides still trail leaders United by six points with five games to go but Cech says Chelsea are the team with the momentum in second place, having won six of their last seven matches.
Gathering pace: Cech believes Chelsea are in with a shout of the title after winning their last seven matches
In contrast, Arsenal have drawn five of their last six and Cech, who has won the championship three times at Stamford Bridge since their London rivals' last success in 2004, claims the Gunners have run out of chances now.
'Arsenal had a big game against Tottenham,' said Cech. 'They were 3-1 up and threw it away. Now they are third for the first time in a long time so let's see how they cope with this new situation. They had plenty of chances this season to close the gap and haven't taken them yet.
'We've been saying for a long time we want to keep winning and maintain the pressure on everybody. Arsenal have difficult games and United have to play us and Arsenal so there could possibly be six points [lost for them].
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'We have two games at home against West Ham and Spurs to come and if we win both, the situation could change again. Chelsea were one of the worst [teams in form] a few months ago and now we're getting back to normal.'
Chelsea were knocked out of the Champions League by United last week but Cech claims it could prove to be a blessing in disguise.
He added: 'They have to play a semi-final, so let's see how they cope. We have one competition to focus on which is to our advantage because we can prepare all week and get more rest.
'Everything is close and it is important to score goals. We could end up with the same number of points, so goal difference will play a big part now.'