"It's fantastic, really fantastic," Copenhagen winger Jesper Gronkjaer said. "We have written history. We fully deserved it."
"We've scored a lot of goals but it's also important not to concede too many so it was frustrating tonight," said Tottenham striker Jermain Defoe, who scored twice.
Group winners are kept apart in the last-16 draw which will be held on Dec. 17, giving potentially easier draws against the runners-up.
Copenhagen will be glad just to be in the draw after advancing for the first time in style by ripping apart Panathinaikos.
Martin Vingaard put the Danish side ahead in the 26th minute by curling a low shot into the bottom right of the net.
Gronkjaer doubled the advantage five minutes into the second half from the penalty spot after being fouled by defender Nikos Spyropoulos.
Barcelona was already assured of top spot and coach Pep Guardiola used the match to watch several reserve players in action.
Andreu Fontas, who was making his European debut, and Victor Vazquez scored the second-half goals that clinched their team's first win in four attempts against the Russian club.
"It says a lot about these players that we were finally able to beat such a good defensive team with people that are so young," Guardiola said.
The first of Tottenham's goals came about in freak circumstances. Peter Wisgerhof's 12th-minute backpass was embarrassingly missed by Twente goalkeeper Sander Boschker as he went to clear the ball upfield.
But Denny Landzaat converted a penalty in the 22nd to level as Spurs conceded the lead three times.
Defoe's second goal three minutes later appeared to have settled the game but Nacer Chadli leveled for Twente five minutes later from a free kick.
While Spurs played a strong side, Inter rested many stars ahead of the Club World Cup and Bremen, which is struggling in the Bundesliga, easily controlled the match.
The goal — only Anderson's second for United — kept the three-time European champions unbeaten in all competitions this season.
Michael Carrick was at fault for the goal, being dispossessed 35 yards from his own goal. Alejandro Dominguez nipped in, took the ball and ran straight at Nemanja Vidic before rolling a pass to Hernandez.
In the other Group C match, Bursaspor and Rangers drew 1-1.
In Group B, Jose Jurado and Benedikt Howedes scored to give Schalke a 2-1 win at Benfica. The Portuguese side clinched a spot in the Europa League after Hapoel Tel Aviv finished bottom by drawing in Lyon.
On Wednesday, AS Roma will be guaranteed progress from Group E if it avoids defeat at lowly Cluj.
In Group H, both spots are open, although Shakhtar Donetsk and Arsenal each need only to avoid defeat to freeze out third-place Braga. Arsenal hosts Partizan Belgrade and Shakhtar plays at home to Braga.
Source: AP News