From there, it was an onslaught.
The goalscorer turned provider, threading through a perfectly-weighted pass for the onrushing Daizen Maeda. It shouldn't have reached him, but the sliding Sam Curtis skewed his interception, allowing the Japan international to slot in.
Adam Idah tapped in the third a minute before the break, with Maeda rounding off a menacing press with his 33rd goal of the season 90 seconds later.
Four goals in 12 minutes as St Johnstone went from dreaming to destroyed.
Simo Valakari's side, who defeated Celtic in the league two weeks ago, would have been forgiven for wanting to hide in the changing room or head back up the road.
Instead, they were forced to suffer through a scarring second half, where Rodgers inflicted further pain by bringing on the likes of Nicolas Kuhn and Jota.
The latter squeezed in a fifth from the acutest of angles moments after an on-field penalty award for James Forrest was overturned by VAR.
That was the second time referee Calum Scott was called to the monitor after the break, after Mackenzie Kirk's spectacular finish at 4-0 was reviewed, then disallowed, on a day that everything that could go against St Johnstone did.