Federer, widely regarded as the greatest indoor player of all time, was given little trouble despite a determined performance from the feisty Serb. The Swiss top seed never had to face a break point as he saw off the world number nine in an hour and eight minutes.
It was Federer's 40th career win at the finals, bettering the record he had held jointly with Ivan Lendl.
Tipsarevic, who qualified for the season-ending finals thanks to Rafael Nadal’s withdrawal through injury, has had his best-ever season, maturing into a top-10 player from the ranks of the also-rans.
While he was as dogged and brave as ever, Federer exploited the still, warm conditions in the O2 as he flicked away a succession of unerringly accurate backhands, winning the key net points while serving with his usual precision and grace.
Next up in Group B is fourth seed David Ferrer, who was allowed to open his finals campaign last of all after winning the Paris Masters at the weekend. In his opener, the Spaniard beat Juan Martin Del Potro 6-3 3-6 6-4.
When asked if he felt skipping last week's Paris Masters was a good decision, Federer replied: "I’ll never find out because I won’t have a chance to go back to Paris and play there.
"I’m happy that I feel fine just in time. I still had some little things that I had to work through the last couple of days, and since yesterday I feel fine.
"I’m happy with my performance today, there’s no pain anymore anywhere, and I am happy with my level of play against Janko, who is obviously a good player.
"It’s nice conditions here, the same as previous years I think. But coming in and knowing I’ve played so well the last year, being at a solid level and liking dimensions of the court...
"I feel like I’m striking the ball well and that it’s a sign of more to come but everything could be so different in my next press conference."
Tipsarevic said he was feeling a little unwell as he slipped to a 0-6 record against Federer, but added that his opponent just played too well.
"I think Roger was just too good," he said afterwards. "I've not been feeling great the past couple of days, but even in previous matches against Roger I wasn't having that much success.
"I definitely won't blame my loss today on my medical situation. I probably would have lost anyway, but when he got early breaks in both sets Roger is probably the best player in the world when he's leading."
Federer usually only needs a break per set indoors, and he got his opening game against serve at the first time of asking as Tipsarevic failed to handle his swooping backhands and, in particular, one majestic gliding volley at the net.
The closest Tipsarevic came to breaking the Federer serve was a sole point at deuce, with the Swiss coming out on top in some marvellous exchanges across the net from both men.
Federer closed out that set in just over an hour, doing likewise in the second set, which was more competitive than the 6-1 scoreline would suggest.
Indeed, Tipsarevic was at times playing magnificent tennis, but everything he threw at Federer was dismissed by the Swiss with disdain.
The best of his three second-set breaks was to go 4-1, as he shaded a breathless rally in which they traded drop shots and flying volleys across the net, before earning break point with a superb disguised forehand, and taking it with a majestic pass down the line.
A swift hold followed and, with Tipsarevic two breaks down and serving to stay in the match, Federer wrapped things up as his opponent made two rare errors, flopping near identical backhand crosses wide.
Having lost so convincingly, Tipsarevic must now realistically beat both Ferrer and Del Potro to qualify for the semi-finals, while Federer is well on his way to a possible last-four clash with either Novak Djokovic or Andy Murray.
He must get past Argentine Del Potro first, a man who has beaten Federer before at the 2009 edition of this tournament, or Ferrer, in fine form after winning in Paris.
"What I didn’t like about that match (against Del Potro) in 2009 was we didn’t know who would go through because it was a matter of games (won)," Federer added.
"This time I have no preference when I play him, but I will try to watch tonight’s match to get some info on how both are playing.
"How has David pulled up after his great win in Paris, how Juan Martin is playing after (winning) Basel? It will be an interesting match-up tonight."
Tuesday's results from the ATP World Tour finals:
2-Roger Federer (Switzerland) beat 8-Janko Tipsarevic (Serbia) 6-3 6-1
4-David Ferrer (Spain) beat 6-Juan Martin Del Potro (Argentina) 6-3 3-6 6-4
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