They join Manly at the top of the NRL ladder on 26 points while the Storm hold down eighth.
The first half was an arm-wrestle with defence from both sides first rate and unwilling to give an inch.
Melbourne backrower Kevin Proctor scored the only try of the half after some handy lead-up work from Smith and Cronk.
That duo, as well as Billy Slater, Will Chambers and Ryan Hoffman all backed up from Wednesday night's State of Origin while NSW halfback Trent Hodkinson turned out for the Bulldogs.
Five-eighth Josh Reynolds missed the match through a three-game suspension for his Origin shoulder charge while Josh Morris sat out injured.
The visitors hit the lead early in the second half when prop Sam Kasiano out-muscled three Storm forwards and stretched out to plant the ball across the line.
Hodkinson added the extras for the Bulldogs to take the two-point lead in the 47th minute.
Melbourne threw everything at the Canterbury side but couldn't find a chink in their armour.
Bulldogs fullback Mitch Brown managed to bat the ball out of the hands of newly-signed Storm winger Marika Koroibete in the in-goal and then pulled off a brilliant tackle to cut down Slater on the burst.
Hodkinson described the win as "ugly".
"We knew it was going to be tough," Hodkinson said. "It was probably our ugliest game of the year but we'll take that win."
- AAP