The Serb, who missed out on the tournament initially as the ninth ranked player, made an immediate impact as he took the opening set 6-2 in emphatic fashion.
But Berdych showed tremendous resilience and character to roar back and take the second set 6-3 before edging out his doughty opponent 8-6 in a final set tie-break in what was a vital victory for the Czech.
Tipsarevic came into the match boasting a 4-1 head-to-head record over Berdych after replacing the injured Murray to take his place in the season-ending tournament, and dictated the play from the outset.
The sprightly Serb broke in the first game of the match with a flurry of ferocious groundstrokes, and proceeded to consolidate his advantage.
Berdych's serve was again dismantled ruthlessly by Tipsarevic in the fifth game, and the Czech was only able to muster two games in a lethargic showing in the opening set.
Tipsarevic appeared to revel in the atmosphere of the O2 Arena and duly thrived as he moved his opponent around the court expertly with guile and intelligent play to take the opening set with consummate ease.
Berdych looked considerably more assured in the second set and both players established themselves with solid service holds which belied the pressure each applied on return.
Eventually it was the Czech player who seized control of proceedings with an inspired game in which a string of rasping groundstrokes forced Tipsarevic under the cosh and clinched the crucial break.
Berdych was unerring as he closed out the set with an assured hold from 5-3, and the London crowd welcomed in a third and deciding set with delight.
The third set was a cagey affair as both players traded blows from the back of the court and worked tirelessly, but neither was able to force a breakthrough as the encounter remained very finely poised.
Indeed, there was not even a glimmer of a potential break of serve until Berdych was forced to repel his opponent from an extended deuce with two enormous first serves down the T eventually closing out the game.
The final set almost inevitably drifted into a tie-break with neither player able to seize the initiative, and at 5-5 there remained nothing to choose between the pair.
But crucially, Tipsarevic went wide with a powerful forehand to hand Berdych a slender lead, and the Serb cruelly slipped while striving for a forehand in what proved to be the final point of the match as the seventh seed sealed victory.
It was a crucial first victory in the tournament for Berdych as the Czech put pressure on David Ferrer and Novak Djokovic at the top of Group A with the pair set to face each other in the evening session.
P W L F A Pts
1. David Ferrer 1 1 0 2 0 2
2. Novak Djokovic 1 1 0 2 1 2
3. Tomas Berdych 2 1 1 3 3 2
4. Janko Tipsarevic 1 0 1 1 2 0
5. Andy Murray 1 0 1 0 2 0 (withdrew to be replaced by Tipsarevic)
1. Roger Federer 2 3 0 4 1 4
2. Rafa Nadal 2 1 1 2 3 2
3. Jo-Wilfried Tsonga 2 1 1 3 2 2
4. Mardy Fish 2 0 2 1 4 0
4. Jo-Wilfried Tsonga 1 0 1 1 2 0