Ninth-seed Tsitsipas battles past Altmaier to reach French Open third round
The Greek ninth-seed, winner at Monte Carlo last month and a finalist in Barcelona, is one of the title contenders, with clay his favourite surface.
He looked to be cruising to an easy win as he raced through the first two sets in less than an hour.
Tsitsipas, a French Open finalist in 2021, pummelled his 83rd-ranked opponent with his powerful forehand before Altmaier upped his game and became more aggressive.
"Fighting yourself. This is something that will happen during a match. You have to fight your emotions and feelings," Tsitsipas said of his loss of concentration.
"The biggest war you have is with yourself. You have to figure that out and get it out of the way. I was down in the score. I didn’t give up. I’ve had plenty of comebacks in the past and I’ve learned from those.
"I remember those and they inspired me to get back into the score and be the type of player I’m looking to be when things aren’t working out so well."
The German, who needed five sets to get through the first round, refused to buckle in the third set, dominating the tiebreak to cut the deficit.
His first break on Tsitsipas' serve put him 4-3 up when his opponent sunk a backhand smash into the net in the fourth with Altmaier pumping his fists.
But the Greek recovered quickly, breaking straight back and seeing out the match a little later on his opponent's serve.
He will next face either Italy's Lorenzo Sonego or Zhang Zhizhen of China.