But things unraveled rather quickly, and suddenly the Flames were staring down a 3-1 deficit.
First, Evander Kane took a beautiful outlet pass from Joe Thornton, stopped at the top of the right circle in a one-on-one battle with Rasmus Andersson, spun, and whipped a shot along the ice that trickled home through the five-hole.
But it was the second one that proved to be the back-breaker.
Rittich came way out of his net to cut off a loose puck and possible breakaway play near the blueline, but fumbled the clearing attempt, allowing Brent Burns to make the steal and slap it home with the goaltender scrambling back in his wake.
"It was a great read by Burns," Tkachuk reasoned. "He's a large, large man that can cover a lot of ground. If it's anyone else on their team, it won't happen. But it was a good read. I've seen Ritter make that play a bunch this year and a few have turned quick transitions into goals the other way. We're not going to tell him not to come out and play that puck."
Rittich's night came to a premature end, as coach Bill Peters turned to veteran Mike Smith the rest of the way.
"We were down two and he didn't look comfortable," Peters said. "Didn't like either goal."
However, his night got off to an discouraging start as the Sharks buried their third of the night just 23 seconds later, with Tomas Hertl supplying the tip on a Radim Simek point blast.
Three shots. Three goals.
"We were turning pucks over and that's when they create their chances, and they did that," said Sean Monahan.
"We were chasing the game from the start.
"I still think we've got a better game to show. We didn't show it tonight. It's an important road trip now and we've got to flip the camera and look forward."
In the front half of the second, the Flames were coming at the Sharks in waves and despite a flurry of chances from the prime scoring areas - including four alone on a mid-period powerplay, Jones them all out.
That critical phase proved costly, as the game settled down and began to tilt back in the visitors' favour soon after.
Kane's second of the night - shelving his own rebound after getting the feed from Joonas Donskoi - put the Sharks up by three at 16:27.
But the Flames got it right back, as the second powerplay unit came up with a clutch goal to make it a two-goal game once again. Justin Braun tried to knock down Brodie's long point shot, but he only got a piece of it en route, tipping it past Jones at 17:42.