Altmaier recovered from a one-sided opening set to beat the Danish star 1-6, 7-6(5), 6-4 in two hours and 14 minutes, booking his place in the second round of the ATP Masters 1000 tournament.
Altmaier turns match around
Rune made a blistering start and raced through the opening set in just 25 minutes, putting Altmaier under immediate pressure.
The German, however, gradually found his rhythm and forced a second-set tie-break. Altmaier held his nerve to win it 7-5, sending the match into a deciding set.
The decisive moment came at 4-4, when Rune dropped serve for the first time in the final set. Altmaier then held his nerve to move to 5-4 and serve for the match.
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At 30-30, the German produced a superb backhand passing shot to create match point before converting the opportunity to complete the comeback.
Shelton awaits in the second round
Altmaier, ranked 67th in the PIF ATP Rankings, will now face fourth-ranked American Ben Shelton in the second round.
The German already has a victory over Shelton this season, having beaten him on clay in Hamburg. That was their only previous meeting before the Shanghai clash.
Shelton arrives in Shanghai after reaching his first Grand Slam final at the US Open last month, making the second-round encounter a major test for Altmaier.
Another setback for Rune
The defeat extends a difficult start to Rune's return to the ATP Tour following the Achilles injury that kept him out for almost a year.
The 23-year-old returned to competitive action in September and helped Denmark in the Davis Cup, winning both of his singles matches against Bulgaria.
However, he lost his opening ATP Tour match on his return in Tokyo to Kyrian Jacquet before suffering another first-round defeat in Shanghai.
Rune, currently ranked 195th using a protected ranking, will now continue his comeback as he searches for his first ATP Tour victory since returning from injury.
Altmaier joins Wednesday's Shanghai winners
Altmaier was one of several notable winners on the opening day of the Shanghai Masters.
Matteo Berrettini, Arthur Fery, Wu Yibing, Tomas Machac and Yi Zhou were also among the players to advance from the opening round.
For Altmaier, however, overcoming a former world No. 4 after losing the opening set represents the biggest statement of the day and sets up an intriguing second-round meeting with Shelton.