Manchester City moved third, two points behind Chelsea, after defeating Swansea 3-0 with two goals by France international Samir Nasri. City has won all seven home matches this season at the Etihad Stadium.
Liverpool's title hopes stumbled as Hull beat the Reds 3-1 its first win in 17 attempts and Manchester United was held to a 2-2 draw at Tottenham.
Chelsea fans were silenced almost immediately after Rodriguez made the most of an error from Michael Essien, who was making his first Premier League start since May 2012. But his mistake was not fatal to Mourinho's team as Chelsea fought back after the interval.
Cahill leveled with a header from close range in the 56th and Terry put Chelsea in front with a glancing header in the 62nd minute for his 34th Premier League goal before Demba Ba put the game beyond reach in the last minute.
"It's very significant for me. It's a huge achievement to maintain it at a top club like I have," said Terry, who has played all 400 games for Chelsea. "I'm thankful for the fans as well for sticking by me."
Nasri's brace and Alvaro Negredo's first half free kick were enough for Manchester City to beat Swansea and maintain its perfect home record in the league, with 29 goals and only two conceded.
City keeper Costel Pantilimon, who was again preferred to Joe Hart in goal, was tested by Jonjo Shelvey before Nasri proved unstoppable in the second half for the hosts.
"Everything is fine at the moment, we had a tough first half but we came back with the best intentions, scored three goals and kept a clean sheet so it's a good afternoon for us," Nasri said. "We have to improve our form away from home. Six points is not a lot, in terms of the gap before we face Arsenal."
Earlier, Jake Livermore and David Meyler scored their first goals this season to give Hull their first-ever win over Liverpool.
Hull went ahead after Jake Livermore's shot from outside the area took a deflection off Liverpool defender Martin Skrtel and looped over goalkeeper Simon Mignolet in the 20th minute at the KC Stadium. Steven Gerrard equalized seven minutes later with a well-placed free kick through a sudden hole in the wall created by Skrtel.
David Meyler put Hull ahead again in the 72nd with a left-footed shot and Skrtel finished a miserable afternoon for Liverpool with a spectacular own-goal header in the 87th.
Liverpool missed England forward Daniel Sturridge who is likely to be out for at least six weeks with an ankle injury.
In the early match, Tottenham Hotspur and Manchester United shared the points at White Hart Lane though Spurs dominated and created the best chances.
Wayne Rooney twice helped the Red Devils come from behind, scoring his second goal from the penalty spot in the 57th minute. The England forward had first leveled from close range against the run of play after Kyle Walker had put Tottenham in front.
"Tottenham had their own pride, which they showed today in their performance," United boss David Moyes said. "I think the big games are all to come in the second half of the season ... There will be a lot of teams now looking to chase them (Arsenal) down and hopefully we will be one of them."
In the wake of Fulham's 3-0 loss to West Ham, manager Martin Jol was fired on Sunday as he paid the price for a disappointing start to the Premier League season.
Fulham is in 18th place and in the relegation zone, having earned just 10 points from 13 games.
Fulham said in a statement on Sunday that owner and chairman Shahid Khan, who bought the team this year, made the decision to part ways with Jol. The club said first-team coach Rene Meulensteen will take over with immediate effect, and will be in charge for the game against Tottenham on Wednesday.
