Federer, who broke Connors' 30-year-old mark with his 161st week at the top of the ATP rankings, defeated Kristian Pless 7-6 (2), 3-6, 6-3 in his first match since taking a month off after winning the Australian Open.
Federer's reign began more than three years ago, when he took over No. 1 on Feb. 2, 2004, after winning his second career Grand Slam title at the Australian Open. Federer said defeating Andy Roddick in the 2004 Wimbledon final was "a huge moment for me."
"Looking back, maybe that was the most important match for staying at No. 1," the Swiss star said during a conference call. "If he would have won that, I think he might have gotten it back."
Connors set his record from July 1974 to August 1977. Connors won eight Grand Slam titles in his 20-year career.
"I haven't heard anything from Jimmy," Federer said, laughing. "I don't know if he's going to talk about it. It's a great record to break, he's had it so long."
Connors now coaches Roddick, who won the first set against Federer in Shanghai in November and had three match points in the second set before falling 4-6, 7-6 (8), 6-4.
"That actually guaranteed me to break the record today," he said.
Federer has another connection to Connors.
When Federer was growing up in Switzerland, he was presented with a watch by Connors during a ceremony recognizing Federer as the best under-14 player in Basel, his hometown. Federer had been a ballboy for an exhibition between Connors and Mansour Bahrami.
"I walked on court, had a picture taken with both of them, and then walked off," Federer recalled. "I was so nervous. Whoever would have thought I would have broke the record? Looking back, it is quite an amazing story."
To commemorate the milestone, a Roger Federer stamp will be issued April 10 in his hometown.
Federer needed time to get up to speed against the 86th-ranked Pless, but extended his career-high winning streak to 37 matches.
"It's always rough here for some reason," said Federer, who won three straight Dubai Open titles before losing to Rafael Nadal in last year's final. "It can happen sometimes when you have not played for a long time."
In other matches, Tomas Berdych rallied to defeat Mohammed Al Ghareeb 3-6, 6-3, 6-2, and Fabrice Santoro beat Tommy Robredo 7-6 (6), 6-4.
The 25-year-old Federer considers Connors' 109 career titles an even bigger accomplishment. Federer has 47.
"He played until he was 40," Federer said. "That's an incredible effort. He definitely marked the game. He's one of the all-time great heroes for all of us."
Federer has been relatively injury-free during his consecutive weeks at No. 1, with only a twisted ankle in recent years. The 10-time Grand Slam champion takes a month off three times during the year _ at the end of the season and after the Australian Open and Wimbledon.
"Scheduling is a very important factor to my success," Federer said. "(The rest) helps me try to heal from injuries and mentally get away."
Federer was asked if he'd heard from his friend Tiger Woods since reaching the milestone.
"Not yet, I'm waiting," Federer said with a laugh.
Federer said he likes the debate about who is the more dominant athlete in their sport.
"He's got it easier, he's playing on grass all the time," Federer said.
Since taking over the No. 1 spot, Federer is 247-15 (.943) with 34 titles in 49 tournaments. He's won six of the last seven Grand Slam titles.
Connors played 61 tournaments during his streak to Federer's 49. During the run, the American won the most titles (12) in 1976, when he went 91-8. Federer won 12 titles in 2006, when he finished 92-5.
Federer is fifth on list of most overall weeks at No. 1. Pete Sampras leads with 86 weeks, followed by Ivan Lendl with 270, Connors with 268 and John McEnroe with 170.