After Scott missed the start of the season with a shoulder injury and Kiwi import Burleigh picked up a knee problem in October, the duo at last linked up in the centres from the start at BT Murrayfield on Friday.
The partnership bore fruit as Edinburgh ground out a 20-8 triumph over Glasgow Warriors, securing a narrow aggregate 1872 Cup victory in the process.
And Scott is looking forward to linking up further with his new midfield partner as the GUINNESS PRO12 season continues towards the business end.
"It could have gone either way but I'm really pleased with the defensive effort," he told the club website.
"I remember saying to him [Burleigh] 'we're not really going to touch the ball' and that's the way it transpired.
"He's the type of player I'd like to play with, he's a good distributer and he's a smart player as well so I look forward to getting a string of games together with him.
"We've beaten a team at the top of the league and that would have been a big boost for us anyway, but because it's Glasgow and because we haven't won the cup in a number of years, I think that makes it all the more special.
"A big win over a big rival, it gives us a lift in terms of the fact that the work we're doing is working and we're going in the right direction. It gives us something tangible to show for it in terms of the cup.
"We'll definitely take confidence next week, going into a tough match to Connacht away."
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