United manager Erik ten Hag fielded a formidable lineup to face Twente, a club that holds special significance for the Dutchman as he rose through their youth ranks and had multiple stints as a player before transitioning into coaching with the Eredivisie team.
Marcus Rashford returned to the line-up after coming off the bench in Saturday's 0-0 draw at Crystal Palace, with Harry Maguire replacing Matthijs de Ligt in defence and Manuel Ugarte taking the place of Kobbie Mainoo.
United had an early let-off when Lammers dragged narrowly wide after slack play by Diogo Dalot, before Twente goalkeeper Lars Unnerstall pulled off a brilliant save to stop Mees Hilgers from turning into his own net.
He was well beaten though by Eriksen's thunderbolt after the ball broke to the midfielder inside the Twente area. Andre Onana turned Sem Steijn's low free-kick around the post near the hour, but Twente drew level when former Rangers forward Lammers dispossessed Eriksen and ran through to fire home.
Unnerstall tipped Joshua Zirkzee's stinging effort over the crossbar and Bruno Fernandes went close, with Unnerstall producing a magnificent reflex save in stoppage time to keep out a Maguire header deflected by Gijs Besselink.
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United ultimately had to settle for an underwhelming point to start the new-look, 36-team league phase that mirrors the format of the revamped Champions League.
Porto, the 2003 and 2011 winners of the second-tier European competition, lost 3-2 away to Norwegian champions Bodo/Glimt, who played most of the second half with 10 men. Ruben van Bommel, the son of former Netherlands international Mark, scored twice for AZ Alkmaar in a 3-2 victory over Swedish side Elfsborg, with ex-Tottenham forward Troy Parrott netting the winner from the spot.
Mauro Icardi's last-gasp goal sealed a 3-1 win for Galatasaray over PAOK in Istanbul, while Nice were left to rue a missed penalty in their 1-1 draw against Real Sociedad. Ander Barrenetxea gave La Real the lead before Pablo Rosario equalised on the stroke of half-time, but Evann Guessand saw his second-half spot-kick saved for the hosts.
Slavia Prague won 2-0 away to Bulgaria's Ludogorets, while Danish champions Midtjylland drew 1-1 with Hoffenheim and Anderlecht overcame Hungarian side Ferencvaros 2-1. Boulaye Dia scored twice in Lazio's 3-0 win over Dynamo Kyiv in Hamburg as both teams had a player sent off.
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