We last met the Roosters in a heart-stopper at Adelaide Oval in Round 15.
A grind from start to finish, both teams scored two tries apiece and it was a goal from the skipper that proved the difference.
The Roosters had 58% of possession in the opening 20 minutes but Storm were rock-solid in defence and held the Tricolours to a lone penalty goal.
Melbourne scored the first try when Kenny Bromwich swung wide on the last for Josh Addo-Carr to race down the left wing, finding Ryan Papenhuyzen.
Cooper Cronk delivered a deft blow in the 27th minute, giving Brett Morris and Daniel Tupou just enough space to cross in the corner, with Latrell Mitchell putting them back in front by two with a conversion from the sideline.
Joey Manu muscled his way over the line in the next play but scores were locked up again in the shadows of half-time when Tedesco fumbled a Brodie Croft grubber back into Croft's path for the young half to touch down.
A try-saving tackle from Mitchell denied Suliasi Vunivalu at one end while a forward pass called back Tedesco at the other.
When Victor Radley was caught in the ruck Cameron Smith duly nudged Melbourne ahead 14-12 from the resulting penalty.
We held the lead for a tense final 10 minutes to record our sixth consecutive win during the representative period and soared to an enviable ladder position - six points clear at the top.