Ole Gunnar Solskjaer’s team came into the match needing at least a draw to advance to the round of 16, but were behind within minutes of kickoff after Angelino beat David de Gea with a fine finish at the far post on a counter-attack.
The Bundesliga side doubled their lead shortly after with Angelino becoming provider this time, crossing the ball for Amadou Haidara to smash home a volley and stake Leipzig to a 2-0 lead they would take into the dressing room at half-time.
Despite the substitution, it was Leipzig who would score again to take a three-goal lead when Justin Kluivert pounced on a loose ball just out of De Gea’s reach and chipped the keeper to pile on to United’s woe.
Looking like they were on their way out of the Champions League, United struck twice in the span of minutes with a Bruno Fernandes penalty and a Pogba header to cut Leipzig’s lead to 3-2.
However, the comeback fell short meaning RB Leipzig are through to the round of 16, while Manchester United were eliminated from the competition.
Paris Saint-Germain, whose match on Tuesday was cut short due to an incident on the sidelines, are also through from Group H regardless of the outcome of their match against Istanbul Basaksehir due to a superior head-to-head record against United.