At the other end of the table, Hoffenheim pipped Bayer Leverkusen and RB Leipzig to fourth place, as they beat Borussia Dortmund 3-1 to secure Champions League Football next season.
Hamburg fans protested at the end of the game.
Dozens of riot police, several on horses, charged on to the pitch and lined up in front of the Hamburg fans, who lit flares and threw them behind the Gladbach goal when it became clear that the team was on their way to the second division.
Most fans reacted with anger to the disturbances, chanting "We are the people of Hamburg and you're not!" and "Get them out!"
The home side were reduced to 10 men as Bobby Wood received a second yellow card for a foul after 71 minutes, but - despite Hamburg's efforts to hold on for maximum points - Wolfsburg's 4-1 triumph over bottom side Cologne meant they could not be caught.
National Hockey League playoffs 2018: Golden Knights vs. Jets preview and prediction
NOTES: Scheifele scored seven goals in Nashville, setting a record for most road goals in one postseason series. The Golden Knights have been a big surprise this year, while the Jets come in having won 19 of their last 24.
Hamburg have been relegated for the first time in their history after 54 years in the Bundesliga.
With Wolfsburg's win long-since confirmed, and no European places for Gladbach to play for, referee Felix Brych eventually restarted the game and then immediately blew for full-time, with Hamburg's teary-eyed players applauding their supporters on a lap of honour.
"It was just a few who have no business in a stadium, " said Christian Titz, Hamburg's third coach of the season.
Stuttgart spoiled Bayern Munich's title party and Jupp Heynckes' last game in charge of the champions by producing a surprise 4-1 success at the Allianz Arena. Their 16th-placed finish in the league puts them into the two-legged relegation playoff against Holsten Kiel, the first leg of which takes place next Thursday.
Freiburg went into the final day vulnerable to being sucked into the play-off spot by Wolfsburg, but their 2-0 win over Augsburg negated that risk, Nicolas Hofler and Tim Kleindienst grabbing the goals.