Thompson broke the deadlock three minutes before the break when he cut in from the left and fired home.
Melbourne doubled their lead in the 66th minute when the striker was pulled down in the box by Ben Sigmund, who was sent off, and Hernandez converted the penalty.
Dani Sanchez drove home from the edge of the box with just under 20 minutes to go for Wellington but Melbourne held on to claim victory.
Gold Coast United also collected their first victory as they downed Newcastle Jets 3-1 at Skilled Park.
Maceo Ritgers opened the scoring after 11 minutes when he blasted home from the edge of the box and Kristian Rees doubled Gold Coast's advantage in the 58th minute when he pounced on a rebound.
Jobe Wheelhouse pulled a goal back for Newcastle when he converted Ryan Griffiths' free-kick but James Brown sealed the points seven minutes from time.