Mouat and Dodds had started the day with a second consecutive win after a splendid four-point haul in the penultimate end secured victory over Estonia.
The Team GB duo – who beat Norway in their opener on Wednesday – were kept honest by the Estonian debutants, but their class ultimately told in the latter stages to force an early end to the contest and a 10-5 triumph.
And it was similar against the Czechs, albeit it was their opponents mistakes, as much as their own shots, that made the difference.
The Czechs ceded the hammer, but reacted well to take a point in the first end. Their ambitious claims for two were only halted by the verdict of the measuring stick.
After that strong start, their callowness showed in the second end, a poor throw by Julie Zelingrova gifting Dodds a chance for three, which she took ruthlessly.
The Czechs cut their arrears to one in the third but the Dodds – who has been in magnificent form so far – restored the three-point gap at the break.
On another day, that might have been decisive, but the Czechs were proving obdurate opposition and – with Mouat a little off his peerless best – the underdogs hauled themselves level.
Dodds delivered again with another two in the sixth before the end that effectively decided the contest. Zelingrova had a throw to thrust the Czechs ahead, but was heavy-handed and instead gifted GB an almost unassailable three-point lead.
Almost unassailable because a rare Dodds mistake offered an opening, but Zelingrova rushed her final thow and could only take two.
That left them agonisingly short but put GB another step closer to exorcising the memories of 2002, when a wretched last-four defeat left them outside the medals.
“We’re exactly where we wanted to be at this stage but we’ve got some tough games in which I need to help Jen out a bit by performing better,” Mouat told BBC Sport.
“I can’t blame the ice – it’s manageable – but I’ve just not figured it out yet.”