Substitute Botti Bia Bi scored a late equaliser when he headed Craig Sibbald's cross beyond Thomas Flynn to conclude an entertaining match.
Flynn was the first goalkeeper called into action as he expertly dealt with a rising shot from Blair Alston and Sean Higgins responded by ensuring Jamie MacDonald was alert in the opposite goal.
Cowdenbeath took the lead late in the first half when Falkirk failed to deal with a throw-in and Higgins found Lewis Milne who scored with a left-foot shot.
Rory Loy equalised for Falkirk early in the second half with a wonderful strike, curling the ball beyond Flynn.
The Falkirk player was then denied twice by the goalkeeper in quick succession.
Higgins put Cowdenbeath back in front, but their joy was short-lived as Falkirk equalised.
Queen of the South looked determined to show they should not be considered also-rans this season and they opened with a comfortable enough 2-0 victory over Alloa.
Derek Lyle opened the scoring when he pounced on a slack passback to force the ball home.
Ryan McCord had a chance for Alloa afterwards but could not put his 10-yard shot on target.
Iain Russell was not far away from a second goal for Queen of the South, but he curled his shot just inches too high.
Alloa looked dangerous on the break and McCord was denied by Zander Clark. The home goalkeeper then kept out in-form Greig Spence before half-time.
Gavin Reilly doubled Queens' lead before the break with a quality finish from the edge of the area.
Queen of the South could have added to their lead in the second half, but seemed content to protect their advantage as the game wore on.
Raith Rovers opened their league campaign with a 3-1 over Dumbarton, but it was not without its cost.
The Kirkcaldy side lost in-form striker Calum Elliot through injury just 10 minutes into the game and did not create too much of note for the remainder of the half.
Raith looked a different side after the interval, however, and took the lead five minutes after the restart when Rory McKeown's long throw was headed down by former Hearts striker Christian Nade to Paul Watson, who drove the ball home from close range.
Ryan Conroy provided the home side with the comfort of a two-goal cushion when he fired home a 20-yard free kick 12 minutes from time and Nade then made it 3-0 with a fine individual effort.
Scott Agnew pulled back a consolation goal for Dumbarton in injury-time.