Qualifier Almagro, 18, challenged the second seed for over two hours and served to force a tiebreak in the final set before bowing out in the first round.
Argentine Coria, returning to action after fitness worries, looked rusty and nervous, particularly in the last set when he was broken when serving for victory.
Almagro, who had the fans on his side after a superb fight, remained in contention until handing Coria two match points by hitting a forehand long.
The Spaniard, who is way outside the top 100 in the ATP rankings, saved the first with a service winner but sent a forehand wide on the second.
Coria, the number two seed, had been nursing abdominal pain and was playing his first match since winning last month's Monte Carlo Masters.
"I didn't know him," he said of Almagro. "He certainly played well."
Russia's Marat Safin had earlier recovered from a sluggish start to squeeze past Sebastien Grosjean 7-6, 7-5.
PHILIPPOUSSIS OUT
The former world number one, twice a finalist in the northern German port city, fought back from 3-0 down in the first set and survived two set points before knocking the eighth-seeded Frenchman out of the claycourt event.
"With a bit of luck he (Grosjean) could have won it in straight sets but I just kept going," Safin said after boosting his preparations for the French Open starting on May 24.
Australia's Mark Philippousis, the 10th seed, followed Grosjean out when Swede Joachim Johansson beat him 7-6 6-1.
Philippoussis, a quarter-finalist here last, is struggling and has not won a match since reaching the fourth round of the Australian Open.
Local hope Florian Mayer provided the first upset of the tournament by knocking out Jiri Novak 7-6 3-6 6-4.
The 20-year-old German, making his first appearance in the event on a wildcard, showed more composure when it mattered to oust the experienced Czech, seeded 15th.
The home fans had more to celebrate when Tommy Haas, staging a comeback after missing last season with a shoulder injury, qualified the easy way. The German was leading Vince Spadea 6-0 when the American withdrew with a thigh injury.
World number one and top seed Roger Federer of Switzerland faces a tough test against Argentine baseliner Gaston Gaudio in his opening match on Tuesday.
