This IS the right way to play it, I only changed one note and switched the zero's 
for fives because it really makes a difference.

D|———————————————————————————————————————————————————|
G|—3—————3———————————————5————3—————3————————————————|
A|—————5———5—3—————————5——————————5———5—3————————————|
E|—————————————5—0—3——————————————————————5—0—3——3—3—|