The Red Devils recorded a 4-1 victory in the first leg of their encounter at Old Trafford last week, putting them in a commanding position to reach the final eight of the competition.
Marcus Rashford scored the only goal of the second leg in the 56th minute, finding the back of the net with a brilliant strike from distance, as Erik ten Hag's side breezed into the quarter-finals.
Edgar Gonzalez, Rui Silva and Aitor Ruibal came into the Real Betis side from the first leg, while Red Devils boss Ten Hag shuffled his pack, with four changes from the weekend draw with Southampton, as Harry Maguire, Tyrell Malacia, Fred and Facundo Pellistri were introduced.
Man United had the first half-chance of the match when Casemiro, who will start a four-game domestic ban against Fulham in the FA Cup this weekend, met a corner from Bruno Fernandes, but Wout Weghorst just could not reach to convert.
Real Betis should have scored in the eighth minute when Juanmi's pace took him clear of Maguire, but the attacker placed his effort wide of the far post.
Joaquin then curled one onto the woodwork from distance in the 11th minute, with Man United coming under pressure from the home side, who were cheered on by a vocal crowd.
Real Betis were the team firmly on the front foot as the first period developed, with the visitors mainly restricted to breakaways through the likes of Rashford and Pellistri.
Fernandes just missed the crossbar with a powerful strike in the 20th minute, before Rashford headed straight at Silva from a dangerous area, only for the offside flag to be raised.
Real Betis had another big chance in the 31st minute when Juanmi raced through on goal once again, but David de Gea was out to make a smart save before the attacker headed the rebound wide.
The home side had another opportunity through Juanmi just before the break, but Maguire made a brilliant block, with the 20-time English champions holding firm in Seville.
Man United then struck the woodwork in the closing stages of the first half, with Pellistri's effort coming off the post, and Weghorst could not make contact on the rebound, with the two teams level at 0-0 at the interval.
Joaquin had the first opportunity of the second period for Real Betis, lifting one over the crossbar inside the first minute, with Man United caught out from kickoff in Seville.
Rashford fired an attempt of his own just too high in the 50th minute, before Fred missed the target from further out two minutes later, as the score remained 4-1 to the Red Devils on aggregate.
Rashford had a brilliant chance in the 53rd minute when he was found by Fernandes inside the penalty box, but the England international could not find a route past Silva, before De Gea made a reflex save to prevent an Ayoze Perez header from finding the back of the net down the other end.
Man United had another excellent opportunity through Rashford moments later, but the forward somehow smashed his effort over the crossbar from close range.
Rashford finally scored in the 56th minute, though, with the Englishman expertly finding the bottom corner from distance after Real Betis had backed off him.
Maguire should have made it 2-0 just past the hour when he met a corner from Fernandes, but the Red Devils captain somehow placed his header wide of the post.
Jadon Sancho, who came off the bench to replace Rashford, placed one wide of the far post in the 64th minute, before Silva did brilliantly to save from fellow Red Devils substitute Marcel Sabitzer.
Silva then denied Weghorst in the 70th minute, with all of the pressure coming from the 20-time English champions, who proved to be far too strong over the two legs.
Anthony Elanga, Diogo Dalot and Victor Lindelof were all introduced off the bench in the latter stages, with Ten Hag protecting some of his players with the tie over in Seville.
Sancho was pleased to see the linesman's flag raised in the 80th minute when he fired straight at Silva from a dangerous position, before Juan Miranda's cross was just too powerful for Juanmi down the other end.
Real Betis should have scored at least once on the night, with Juanmi having a host of opportunities, but the La Liga outfit were ultimately unable to find a way past De Gea.
Man United will now switch their attention to the FA Cup, preparing to welcome Fulham to Old Trafford in the quarter-finals of the competition on Sunday, while Real Betis will resume their La Liga campaign at home to Mallorca on the same afternoon.