The left-back scored two sublime free kicks to bring the Toffees back into contention before the Chelsea loanee wrapped up three points with a powerful header
The Toffees trailed twice at Upton Park to goals from Ravel Morrison and Mark Noble but a pair of superb free kicks from Baines brought Martinez's side level.
Lukaku was introduced at half-time for the anonymous Nikica Jelavic and responded by heading home a late winner after the Hammers were reduced to 10 men.
Speaking to reporters, Martinez hailed the brilliance of Baines: "We are well aware of the quality he has - the first free-kick will show you that, but where Leighton takes it to a next step, he’s capable of taking another free kick with a world class keeper with experience, and score.
"Similar technique but a different free-kick. There are many around the world who can take good free-kicks but when you put Leighton in that position for a second time and being able to do that is quite unique.
Baines dumbfounded Jussi Jaaskelainen by curling the first dead ball into the Finn's top-right corner before striking the second in off his left-hand post, leaving Martinez labeling him as the difference between winning and losing.
"He has such a cultured left foot," Martinez continued. "I have seen many great takers, but Leighton puts it wherever he wants from that sort of distance. It’s an unbelievable quality to have. It’s difficult to compare.
"Sometimes you get good work from the goalkeepers or the wall. But you know that ball will go where he wants it to go. His dead ball qualities are unique.
"But the most impressive aspect is taking two from the same spot and they’re both completely different, both finish in the back of the net. He was influential and the difference between getting a win or not."
Martinez was also indebted to Chelsea loanee Lukaku, who came off the bench at the interval to make his debut and grab a winner with five minutes to go, leaving the Spaniard equally effusive with his praise.
"Romelu is the type of striker who influences everyone around him, from the opposition to the gaps he creates," Martinez commented.
"Mirallas became a threat all of a sudden with his pace behind. the goal is everything that typifies Lukaku - that desire and that character to want to be successful. That’s why he’ll be such a big asset for us.
"He comes on, scores the winner. His work rate, he understands how we want to play, he is a very, very intelligent footballer. All I want is for him to carry on and go from strength to strength. His potential is incredible."
Martinez also clarified the Belgian's situation at Everton, stating that Chelsea could not recall the striker.