The Germany playmaker scored two and had a hand in creating the third, showing Wednesday's Champions League semi-final opponents Borussia Dortmund they have more to worry about than simply stopping Real's Portuguese goalscoring machine.
Jose Mourinho's side have to travel for the first leg, when Ozil's pace and defence-splitting passes will be crucial to the Spanish club's hopes of going on to tilt for a 10th European crown.
"Ozil is one of the great players who is under-rated in the Spanish league," Betis coach Pepe Mel told a news conference.
"He's at the same level as Cristiano Ronaldo and Lionel Messi, only he doesn't score the same number of goals. He's a star."
Ozil, 24, has often been questioned for his failure to get on the scoresheet more often and his two goals against Betis took his tally in La Liga this season to eight.
Where there is little doubt, however, is his ability to carve openings for his colleagues and he is the side's leading creator of goals in the league with nine assists.
He has one goal and four assists in the Champions League.
Against Betis, he unlocked the visiting defence by dribbling off the right wing in the 45th minute and exchanging passes with Karim Benzema as he curved in to the area.
Through one-on-one with the keeper, he shaped to shoot across the face of the goal and wrong-footed him with a delicate shot inside the near post.
Ozil led a classic Real breakaway for their second goal as he raced from deep in his own half and fed Ronaldo wide on the left. The Portugal forward played in Benzema to make it 2-0.
At the end, Ronaldo's deep cross was volleyed goalwards by Jose Callejon, and Ozil swept the ball high into the net from close range a minute after Betis had been denied an equaliser as a shot hit the crossbar and was then cleared off the line.
"We all know the player he is and what he can create, even when he isn't as brilliant as usual," Real's assistant coach Aitor Karanka said.
"He didn't play in Bilbao last week because of a minor complaint and it was important to see him play a full 90 minutes against Betis. He has played a great game.
"He now has time to recover. It was good for him to get his touch back and build his confidence."
