The 20-year-old, on loan from Chelsea until the end of the season, nodded home the 84th-minute winner but his overall contribution was just as crucial.
"Romelu is the type of striker that influences everyone around him because of the gaps he creates. Other players around him become a threat," Martinez said.
"The goal is everything that typifies him - the character and desire to want to be successful. That's why he will be such a big asset.
"He's a very intelligent footballer and I want him to continue enjoying his football because his potential is incredible."
Lukaku was knocked out briefly in the act of scoring after clashing heads with Joey O'Brien but Martinez - who confirmed he cannot be recalled by Chelsea - dispelled any concerns over his health.
"For a second we were worried, but after 10-15 seconds he was fine," he said.
Everton equalised twice through the dead-ball skills of Baines, who beat Jussi Jaaskelainen twice with free-kicks.
"We are well aware of the quality Leighton has. The first free-kick shows that," Martinez said.
"Where he takes his quality to the next level is by scoring with a completely different type of free-kick. That's what makes him special.
"Many players around the world are good at free-kicks, but he's able to do it a second time. Leighton places the ball wherever he wants at that distance. I think he's unique."