Ayoze Perez's strike cancelled out Marcus Rashford's opener to leave the two teams level at the interval, but the Red Devils scored three more in the second period through Antony, Bruno Fernandes and Wout Weghorst to claim a strong advantage ahead of the second leg in Seville next week.
Man United head coach Erik ten Hag named the same XI that started the seven-goal loss to Liverpool at Anfield on Sunday, with the Dutchman looking for a response from his players in the European affair.
Betis were captained by 41-year-old Joaquin, and there was interestingly no spot in the XI for either leading goalscorer Borja Iglesias or fellow forward Willian Jose, with on-loan Leicester City attacker Perez chosen by head coach Manuel Pellegrini to lead the line.
Man United had the ball in the back of the Real Betis net in the fifth minute through Weghorst, who converted from a Fred cross, but the goal was disallowed due to the latter being offside.
The Red Devils did score in the sixth minute, though, and it was an emphatic finish from Rashford, who worked a yard of space inside the penalty box following a loose clearance before smashing the ball past experienced goalkeeper Claudio Bravo.
Weghorst then tested Bravo with a diving header in the ninth minute after meeting an inventive cross from Casemiro, with the home team looking to double their advantage early on.
Weghorst had another opportunity in the 17th minute when the experienced forward met a low cross from Luke Shaw, but his effort was deflected just wide of the near post.
Bravo then had to be quick off his line to prevent Rashford from having the chance to make it 2-0, with the former Manchester City goalkeeper just about doing enough to deny the in-form attacker.
Weghorst had another huge chance in the 27th minute when Antony picked out his teammate inside the box; he somehow missed the crossbar from close range, although the forward was in an offside position.
Bravo then kept out a curling effort from Rashford before Fernandes had one deflected wide of the post, with the 20-time English champions looking dangerous every time that they broke forward.
Casemiro was next to try his luck for the Red Devils, hooking over the crossbar from inside the box after Betis had failed to deal with a corner kick.
Against the run of play, the visitors were level in the 32nd minute of the contest, with Perez expertly finding the bottom corner from a wide position after Juanmi had picked out the Spaniard.
There was a check on a possible Juanmi handball, but the goal was given, as Betis equalised with their first shot on target at Old Trafford, much to the frustration of the home side's supporters.
Man United had a chance to score a second in the 41st minute when Rashford broke into the Betis box before picking out Antony, but the Brazilian failed to make proper contact, and Bravo was on hand to collect.
Betis then had a shot deflected onto the post down the other end, with a poor kick from Man United goalkeeper David de Gea putting his team in trouble, and Perez's effort hit Fernandes before striking the woodwork.
The home side regained the lead in the 52nd minute, and it was a wonderful strike from Antony, who worked the ball onto his left foot before expertly curling one into the far corner of the net.
Man United then scored a third in the 58th minute, with Fernandes, who has faced heavy criticism in recent days following the loss at Liverpool, heading a corner from Shaw into the back of the net; Bravo got hands to the ball but was unable to prevent a third for the Red Devils.
Bravo managed to keep out a low effort from Antony just before the hour, before the Brazil international scooped one just over the crossbar following a brilliant pass from Fernandes.
Betis' goalkeeper then saved from Fred in the 68th minute, before Fernandes was booked for a late challenge on Bravo when he was racing to reach a through pass.
Weghorst had one blocked into the arms of Bravo in the 76th minute, before the Betis stopper did brilliant to keep out an attempt from Antony, who had been played through by Weghorst.
Finally, Weghorst had his first Old Trafford goal in the 82nd minute, with the striker converting from close range after Bravo had denied Scott McTominay, with fellow substitute Facundo Pellistri doing brilliantly to find the midfielder inside the box following a corner.
Casemiro missed the post with a low effort late on, before Martinez and Pellistri came close with attempts in stoppage time, as Ten Hag's side declared at four on Thursday night.
Man United's performance was far from perfect, with the Red Devils looking nervy at the back in the latter stages of the first half, but it was an excellent second-half display, with Ten Hag getting the response that he would have been demanding following the shock result at Anfield.
The hosts will now switch their attention back to the Premier League, with Southampton visiting Old Trafford on Sunday afternoon, while Betis will return to La Liga action on Sunday with a trip to Villarreal.