Hearts' top scorer struck early to set the Jam Tarts on their way and scored his second from the penalty spot and Gretna could not respond.
Davie Irons' side finished the game with ten men after Danny Hall was sent off midway through the second half after picking up two bookings.
Velicka had a chance for Hearts in the opening minute but Gretna goalkeeper Greg Fleming forced him wide and the Lithuanian striker could only fire into the side-netting.
But the goal was only delayed. Michael Stewart set up Velicka again and he cracked an unstoppable shot high into the net from just inside the box in the third minute.
Hearts dominated the early stages with Stewart seeing a lot of the ball in midfield.
But Gretna had an opportunity to equalise after 13 minutes when Kenny Deuchar outjumped the Hearts defence to get on the end of Gavin Skelton's cross but he could only send his header over the top.
Hristos Karipidis almost made it 2-0 with a terrific header from an Andrew Driver cross but Fleming made a wonderful save to claw the ball for a corner.
The goalkeeper then did well to touch a left-foot shot from Ruben Palazuelos past his post.
Three minutes from the break, Hearts were awarded a penalty when Hall pulled down Velicka in the box and the striker took the spot-kick himself to fire it beyond Fleming.
The second half followed a similar pattern with Hearts piling players forward in an attempt to kill off the game.
Gretna enjoyed a decent spell midway through the second half and Steve Banks was called into action to beat away a well-struck effort from Mickael Buscher.
Gretna were reduced to ten men after 65 minutes when Hall picked up his second booking of the match when he fouled Andrius Ksanavicius.
Substitute Saulius Mikoliunas should have made it three with 15 minutes left but shot straight at Fleming with Gretna stretched at the back.
Velicka should have completed his hat-trick when a long ball from Christophe Berra beat the offside trap but he tugged his shot wide with only Fleming to beat. He managed to get the ball in the net right at the death but was ruled offside.