Joshua Zirkzee rose from the bench to make his Red Devils debut and he scored the only goal of the game in the 87th minute at Old Trafford.
That was the moment of the match but Martinez and Traore provided some entertainment in the first half as they each got the better of each other at times.
The rapid Fulham winger steamed past the Argentine to get into a good position early on, and while it came to nothing, it was an alarming passage of play for the United man.
However, the excellent defender learned from that moment and next time Traore tried to go past him he was wholly unsuccessful as Martinez won the ball and left the winger on the floor.
Looking at footage of the Spain international on the deck after their challenge, Martinez told Sky Sports: ‘I sent him to the gym!’
The Manchester United man added: ‘He is difficult to play against and I learned from the first situation, in the first situation he killed me but then I killed him back.’
Manchester United were not entirely convincing but they did create a few good chances and deserved the victory, kicking off the season with an important win.
‘For sure it is really important and the most important thing is the three points – we still have to improve a lot,’ Martinez said, after playing at centre-back and filling in at left-back at times.
‘It is difficult to play for this big club, but we live for that and we have to play in a positive way. We have to take this pressure and like today we had a good connection with the subs and fans as well – I am proud to play for this club.
‘I didn’t play many games as left full-back, but as a player you have to give everything to the team. If the team needs me there I will give everything. If I have to play there I will give everything.’
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