The Costa Rican full-back was among the goals for the second time in as many outings on Wednesday, as he built on an impressive showing against Stoke City with the decisive effort during a trip to Manchester United.
His solitary strike earned the Toffees their first success at the Theatre of Dreams since 1992 and consolidated their standing just outside the Premier League's top four.
Breaking into that pack is now the target for Roberto Martinez's side, and a buoyant Oviedo is convinced that they can force their way into UEFA Champions League reckoning.
He told the Liverpool Echo on his midweek heroics and Everton's ambition heading forward: "It's the biggest goal of my career, against one of the biggest clubs in the world. It was special for me.
"I'll never forget it, but I also think the best moment is coming.
"I think the aim now is the Champions League. Anything is possible.
"Copenhagen played in it when I was there, but I was on the bench so I'd love to play in it for this club. The most important thing now is we keep going."
Oviedo, who joined Everton in the summer of 2012, has spent much of his time at Goodison Park playing back-up to Leighton Baines, but is determined to make the most of his moment in the spotlight as the England international nurses a broken toe.
He added: "I've worked for a long time and waited for my opportunity.
"It's difficult being on the bench for a year but I tried to work hard and put in extra hours.
"Now the opportunity has come and everything is good. I'm happy I have scored two goals but I need to get better every time I play also."
Oviedo's next outing is likely to come against table-topping Arsenal on Sunday, and the 23-year-old says he and Everton will head to Emirates Stadium confident they can secure another notable scalp.
He said: "Arsenal are the top team and they play the possession game better than anyone.
"But we need to keep focused and play like we did here. If we can win at Old Trafford, we can win there."