Elsewhere, Juventus want to end a long European wait for a win, Valencia are determined to continue a victorious run, Lille are in danger of being eliminated and Galatasaray and Benfica's hopes are also in the balance.
Celtic boss Neil Lennon has promised a 'special evening' when his side take on Spanish heavyweights Barcelona in Group G in the wake of earlier this week celebrating the club's 125th year anniversary.
But Tito Villanova's visitors can qualify with another win over their Scottish rivals, who suffered a tough, late defeat at Camp Nou on Match Day Three.
And the Catalans are confident after losing just three of their last 25 away games in the Champions League.
Barcelona also arrive as the only team to have beaten Celtic, who themselves could take a giant step towards the last 16 with a famous win, at home in the Champions League in 21 matches.
100 per cent record
Like Barcelona, Manchester United have a 100 per cent record in this season's group stages and another win at Braga would see Sir Alex Ferguson's team into the knockout stages.
Last season's Premier League runners-up suffered the embarrassment of going out in the groups in 2011/12 and they have been determined not to make the same mistakes in the current campaign.
Jose Peseiro's Braga, though, are involved in what could be a three-way battle for second place in Group H and they are particularly keen to make amends for blowing a two-goal lead in a 3-2 defeat at Old Trafford.
Chelsea have made unconvincing work of their defence of the Champions League and another slip up against Shakhtar Donetsk would be unthinkable.
Having lost in Ukraine, Roberto Di Matteo's side have just four points from three matches and the Italian knows his team's remaining games in Group E are 'must-win'.
Chelsea cannot be eliminated on Wednesday night but any more dropped points would prove very costly ahead of remaining fixtures against Juventus in Italy and Nordsjaelland in London.
Lille could be knocked out on Matchday Four after failing to take a point so far in Group F.
A trip to in-form Bundesliga leaders Bayern Munich, who have won 15 of their last 16 home European games, is therefore far from ideal.
In Group F's other game, Valencia will aim to put a three-point distance between themselves and BATE Borisov, who were defeated by a Roberto Soldado hat-trick in Minsk.
Nordsjaelland, Benfica and Galatasaray have all only recorded just one point in Groups E, G and H, respectively, and they know they are in danger of being knocked out if they do not quickly start winning.
Danish minnows Nordsjaelland face a difficult task in picking up three points when they take on Juventus in Turin.
But they did hold the defending Serie A champions to a draw in Copenhagen in the reverse fixture, which was the Italian club's ninth in succession in Europe.
Benfica will hope to fall back on historically strong home form when they host Spartak Moscow but, having lost to Barcelona in Lisbon and Chelsea in last season's quarter-finals, they will be worried about suffering three home defeats in a row in Europe for the first time in their history.
Galatasaray's hopes of reaching the last 16 also look slim and ahead of visiting Cluj they have not taken three points away from home in the Champions League in more than 10 years.