Tipsarevic has been unwell for the past few weeks but was determined to feature in the prestigious season-ending tournament after cracking the top 10 and qualifying following Rafael Nadal’s withdrawal.
The flamboyant Serb was not at the races in the first set but showed something closer to his 2012 form in the second - form which saw him rise from the Challenger circuit to a top-10 player in his late 20s.
Argentina’s Del Potro just had to put in a solid if unspectacular performance, although he encountered more resistance in the second set, which he closed out with a comfortable hold to claim victory in one hour and 17 minutes.
Roger Federer had already qualified for the semi-finals after beating David Ferrer, but all three are still in the hunt, provided results go their way, although eighth seed Tipsarevic is an outside bet at best after failing to take a set in his first two matches.
Tipsarevic ‘s straight-sets defeat to Federer was not helped by a cold, not to mention a general end-of-season fatigue that led to his undergoing blood tests following the Paris Maters.
On this performance his “medical condition” – as he called it – had worsened, although an awful first set was improved upon in the second.
"I'm playing horrible, I'm playing worse than horrible, I'm playing the worst tennis that I played in a long time," was the Serb's brutally honest assessment of his tournament so far.
The Serb’s match started dreadfully as he double-faulted and mis-hit his way to a love break. It did not get any better as he failed to hold serve once, sixth seed Del Potro playing within himself as he completed the dreaded bagel in 28 minutes.
The stats told it all – in the first set, Tipsarevic only landed 43 per cent of his first serves, and won a measly 15 per cent of those on second serve.
The misery looked set to continue in the second as the Serb fell 30-40 in the opener. But, off deuce and via another double fault, he managed to scramble his first hold of the match.
That steadied the sinking ship somewhat and, while he did not challenge Del Potro’s next service game, he was able to boost his confidence with a love hold.
Del Potro, meanwhile, was lying in wait for an error, happy to do most of his work from deep as he got the crucial break at 3-2, Tipsarevic going long with a double-handed backhand.
Tipsarevic is a fighter though, and he displayed his battling qualities to hold off deuce with a fantastic selection of volleys at the net as Del Potro used all his power to try and pass him.
But it was too late, and with Del Potro able to control most of his points off a solid first serve, the Argentine closed out victory to keep his semi-final hopes very much alive.
He probably has to beat Roger Federer first though, and having done so here in 2009 and only a few weeks ago in the Basel final, he is better-placed than many would be in such a situation.
"I need to beat Roger once again, it's going to be a different match like 2009 here, but also is going to be a special match for me," Del Potro said afterwards.
"It could be my last match in this season, so I will try to play similar to Basel, trying to be more aggressive than him all the time and see if I have little chance to beat him."
Tipsarevic, meanwhile, is unlikely to claim the straight-sets win over Ferrer he would need to qualify, but he will be able to look forward to starting next season as one of the world's top players, unthinkable this time 18 months ago.
2-Roger Federer (Switzerland) beat 4-David Ferrer (Spain) 6-4 7-6(5)
6-Juan Martin Del Potro (Argentina) beat 8-Janko Tipsarevic (Serbia) 6-0 6-4