It's the Capital side's fifth win on the trot since their opening-day defeat at Dalbeattie Star last month.
It was the visitors, however, who opened the scoring at Christie Gilles Park through Jack Blakie's 14th-minute strike.
But Strollers hit back with three goals before the half-time interval, Alieau Faye equalising from the spot, and then Joao Balde and Andy Johnston turning the game on its head.
The hosts really turned on the style in the second half, both Balde and Faye adding to their individual tallies with Jonny Moffat and a trialist also on the scoresheet.
Delighted boss Gary Jardine said: "We started the game really well and despite going a goal behind, the players were excellent and responded really well. Our target is to get to 30 points as early as possible so to have half of that after six games is pleasing, especially given the disappointment of losing the first game of the season.
"While you don't get anything for being top at this point, it's nice to see and a reward for the hard work that everyone at the club have put in over the close season. It can only give the players confidence for some tough games ahead."
Bonnyrigg Rose are hot on their heels in third after they came from behind to see off Caledonian Braves 2-1 at Alliance Park.
Luke Main's solo effort had Braves ahead in the fourth minute, but Rose responded and were level seven minutes later through in-form George Hunter, stabbing home from close range after Keiran Hall's effort had come back off the woodwork.
The visitors carved out numerous opportunities to assume the lead and were finally rewarded with 11 minutes left to play when Dean Hoskins got his head on the end of Lee Currie's corner.
Manager Robbie Horn said: "I'm delighted to get three points. We didn't start the game well and gave away another cheap goal which is frustrating, but we got ourselves back in the game, although we never really took control even after we scored.
"But I thought the second half we performed better, had more chances to score but didn't take them and I thought it was going to be one of those days. But Dean has popped up with a fantastic header. We managed to grind it out but it's going to be like that this season."
Elsewhere, Spartans' fine form continued with a 2-0 success over Broomhill at Ainslie Park.
Dougie Samuel's side are fourth following their fourth successive victory – a run that has also seen goalkeeper Blair Carswell yet to concede since the defeat to Rangers B on the opening day.
Scott Maxwell teed up striker Blair Henderson to score his fifth of the campaign on the half-hour mark and the visitors' task became even harder when Jack MacCalman was shown a straight red for a last-ditch tackle on Jamie Dishington.
Dishington got his revenge with 20 minutes remaining when he added a second after an error by the Broomhill goalkeeper.
And Edinburgh University picked up their second point of the season following a 1-1 draw with Gala Fairydean Rovers, both goals coming in the first half at East Peffermill, the Uni's Ben Spellman's header cancelled out by Alieau Touray.