Bidding to banish the demons of major tournaments gone by, Die Mannschaft made an early statement of intent with first-half goals from fledgling talents Florian Wirtz and Jamal Musiala, as well as a cool Kai Havertz penalty.
Scotland's Ryan Porteous was sent off for his role in the latter goal - an incident which summed up the visitors' atrocious first-half display - before Niclas Fullkrug made it four as the plight of Steve Clarke's side continued.
An Antonio Rudiger own goal was a marginal blot on the Germans' notebook, but Emre Can restored the hosts' four-goal lead with virtually the last kick of the game, earning the magnificent Mannschaft the biggest opening win that the Euros has ever seen.
While Germany settled into a period of early possession, Scotland's backs-against-the-wall approach was initially paying dividends, as Clarke's men were standing their ground and not diving into tackles.
However, the Scots' frailties were exposed in the 10th minute as Wirtz struck the first goal of the tournament; a fabulous switch of play from Toni Kroos to Joshua Kimmich ended with the Bayern Munich man picking out Wirtz on the edge of the D, and the playmaker beat Gunn all ends up with a calm first-time finish.
Gunn did get a hand to Wirtz's effort - which was not right into the corner - but could only help the crisp strike on its way into the net via the post, as the 21-year-old became both Germany's youngest Euros scorer and the youngest scorer of an opening goal at any European Championships.
Deserved red card epitomises shocking Scotland first half
The German record was almost immediately snatched away from Wirtz just nine minutes later, as Kai Havertz elected not to shoot from a promising position in the left-hand side of the box and instead laid off Jamal Musiala, who rifled in the hosts' second into the roof of the net.
The ex-England youth international was proving too hot for the Scots to handle and won his side a penalty in the 25th minute - or so he thought - as Ryan Christie clumsily felled him right on the edge of the box, but Clement Turpin's decision was overturned after a VAR review; the offence had taken place just outside the box.
Havertz's low free kick was meat and drink for Gunn, but the Arsenal man would get one set-piece right in the 45th minute, where Scotland's nightmare evolved into a full-blown crisis as Porteous deservedly took the walk of shame.
After the Barcelona man had a header well saved by Gunn, Porteous denied him a shot at the rebound with a disgusting tackle off the ground - catching his counterpart with his studs on his ankle - giving Turpin no choice but to send him off after a check of the monitor.
Havertz, after a short stutter, stepped up and extended Germany's lead against the 10 men of Scotland, whose head coach Clarke was forced to sacrifice any slim hopes of a shock renaissance, bringing on Grant Hanley for the anonymous Che Adams at half time.
Normal service resumed thereafter, and Die Mannschaft should have been four goals to the good in the 58th minute as Wirtz latched onto a Maximilian Mittelstadt cross to the back stick, but his half-volley sailed over the top.
The 21-year-old's successful evening then came to an end, but Nagelsmann's substitutes were in an equally prolific mood, and goal number four arrived for the glittering Germans in the 68th minute, as Fullkrug fired in an unstoppable 20-yard strike into the top corner following a lucky break off of Hanley.
The same unorthodox combination linked up for what Fullkrug thought was his second and Germany's fifth in the 76th minute, as Hanley's attempted clearance hit Fullkrug, whose shot was saved by Gunn before bouncing over, but Scotland were saved by the offside flag.
There was something for the Tartan Army to cheer right at the end, though, as Germany failed to deal with an 87th-minute Andrew Robertson free kick, and Scott McKenna capitalised at the back post with a header that took a wild deflection off of Antonio Rudiger and deceived Manuel Neuer.
However, Neuer and co had smiles on their faces once again deep into added time, as Can - who was only called up to the squad due to Aleksandar Pavlovic's withdrawal - was given too much time and space to curl home from 20 yards; Gunn got fingertips to his strike but was otherwise powerless.
What next for Germany and Scotland?
Both sides now have five days to recover from their Munich exertions before their second Euro 2024 matches, as the tournament hosts face Hungary at the MHPArena in Stuttgart on June 19, a couple of hours before Scotland clash with Switzerland in Cologne.