With the England international likely to be sidelined by a broken toe well into next month, his Costa Rican deputy has made an instant impact in his two appearances.
The 23-year-old last weekend marked only his second league start for the Toffees in 18 months with a goal in the 4-0 thrashing of Hull but then went one better in midweek with the strike which brought their first Premier League win at Old Trafford in 21 years.
Speculation still persists that United manager David Moyes will return to his former club to sign Baines in January after a failed bid in the summer.
And while Oviedo's performances may have given Martinez confidence they can cope without Baines that does not mean he is willing to let his first-choice left-back leave.
"Nothing changes. We are in the middle of the season, we have just gone 14 games and the only thing we are thinking about is finishing the season with the strongest squad possible," said the Spaniard.
"The last thing we want is to lose experienced players, players who mean a lot to Everton and who represent a lot in terms of what we want to achieve."
Nevertheless Oviedo is set for an extended run in the side and has found himself catapulted into the limelight.
In scoring at Old Trafford, he not only became the club's joint second-highest league scorer this season - alongside Baines, right-back Seamus Coleman and midfielder Ross Barkley - but won himself a new legion of fans.
Martinez said the defender was gaining his reward for being patient and committed.
"We had many phone calls from Costa Rica. The game was live there and his hero status has gone to a different level so it doesn't surprise me how he is affecting people at the moment," said the Toffees boss.
"The assessment (of him) is exactly the same as I had in pre-season: I thought he came back ready for this campaign showing he was ready to cope with the physicality of the British league.
"In pre-season he played in many games and showed he was ready but has had one of the toughest jobs you can have fighting for a position with someone like Leighton Baines, who is in the best moment of his career.
"It has been probably frustrating for him at times but it is an incredible example of how you should behave as a footballer - just working hard, being ready and when you get the opportunity show you can help the team.
"Everyone is delighted for Bryan because he is getting what he deserves, it is not an accident.
"Now it is a great position for us to have such strong competitiveness for that position."
While the left-back area has been strengthened, Martinez is looking to strengthen other positions next month to cover long-term knee injuries to striker Arouna Kone and midfielder Darron Gibson.
"We are going to use the window in January to try to help the team because we lost two players for the long term," said the Spaniard.
"Arouna and Darron are two very important players for us so we will try to see if we can identify one or two players that can help the group.
"We have been working hard to identify who can help the group and that is what we are looking for in January."
Martinez admits his initial fears Kone would not recover from an operation to repair damaged cartilage in time to play a part in the remainder of the season have materialised.
"Arouna started the first part of his recovery and it is going to be long-term, as expected," he added.
"I don't think we are going to see Arouna this season.
"If we can get him back for the final two months he will have done really well.
"There was a big chunk of cartilage that had to be repaired in his knee.
"We are very pleased in the way everything has been done but it will be difficult to see him this season.
"In the same manner we are hoping we can see Darron Gibson before the season ends but clearly it is a long-term injury as well."