The Blues stopper claimed a milestone shut-out as his side saw off Steve Bruce's Tigers to climb to the top of the Premier League
The Chelsea goalkeeper surpassed the previous record held by Peter Bonneti, who spent 20 seasons at the club between 1959 and 1979.
Cech, though, has overtaken Bonneti's record in only his tenth season at Stamford Bridge, having joined from Rennes in the summer of 2004.
The Czech international has been a virtual ever-present during his time at Chelsea, playing a vital role in the three Premier League titles, four FA Cups, Europa League and Champions League trophies amassed over the previous decade.
Speaking to BT Sport after Saturday's clash, Cech was keen to keep his focus on the acheivements of the team. "The important thing is that we keep winning games, we keep winning trophies," he said. "We want to win the league. Hopefully the clean sheets will halp us to achieve our targets.
"The most pleasing thing about all this is that we won a very important game," he continued. "Now we are top of the league for the first time in a long time, and we hope to stay there as long as we can."
Cech, whose record-breaking clean sheet was also his 150th in the English top flight, is now only 20 short of for the all-time Premier League record, currently held by David James. James clocked up 170 clean sheets over his 18 seasons in the division.