Defenceman Daniel Tjarnqvist also scored for Edmonton and Jarome Iginla replied for Calgary in a penalty-filled affair before 16,839 fans at Rexall Place. The team play again Saturday night in Calgary.
It was the 29th time the 29-year-old Sykora had scored twice in a game in his 10-season career. He has yet to score a hat trick.
Miikka Kiprusoff made 19 saves for Calgary in a game that featured numerous end-to-end rushes and forced both goalies to make spectacular saves on two-on-ones and against one-timers from close in.
Sykora opened the scoring with about five minutes to go in the opening frame after winger Ales Hemsky drove hard to the net, then tried and failed to beat Kiprusoff on the backhand. The puck rebounded straight out and Sykora swooped in to bang it home.
He scored the eventual game-winner three minutes later with the Oilers on a two-man advantage, taking a Jarret Stoll pass in the high slot and one-timing a low slapshot past Kiprusoff.
The Flames wasted a golden opportunity in the first period when Iginla was taken down on a breakaway by defenceman Marc-Andre Bergeron and awarded a penalty shot.
On the shot, Calgary's captain tried a backhand deke but Roloson stayed with him laterally across the crease for the pad save.
Tjarnqvist sealed the Oiler win midway through the third period, again on a play initiated by Hemsky.
The Czech winger used his speed and shifty moves to penetrate the Flames' defence, then turned and dished the puck to Tjarnqvist, who wristed a shot from the left faceoff circle over Kiprusoff's shoulder and into the top far corner of the net.
Iginla broke Roloson's shutout with just over five minutes left in the game with a snap shot from close in after taking cross-ice pass from Daymond Langkow.
Sykora, normally a right winger, has been shifted to second line centre between Hemksy and Raffi Torres given the depth the Oilers have up front.
The six-foot 190 pound Czech signed in the off-season with the Oilers as an unrestricted free agent after splitting last season with the New York Rangers and Anaheim Ducks.
Notes: Prior to the game, the Oilers raised their 2005-06 conference championship banner amid crowd cheers and a light show. The Oilers themselves, however, stayed in their dressing room a The Oilers are 14-9-4 on opening night while Calgary is 11-13-10 ... Oiler forward Ryan Smyth didn't practise Wednesday due to a strained neck but took a regular shift in Thursday's game ... The Oilers have said they're using the Flames as a measuring stick this season. They were 3-5 against the Northwest Division champs last year and a woeful 1-4-1 the season before that.