After falling behind to a bizarre 55-yard goal, they had been struggling to break out against determined non-league opposition before using the storm as cover.
In their short League career, Rushden had collected three points on three of their four visits to the Memorial Stadium. They found the incentive to raise their game again when Marcus Kelly put them ahead in the 11th minute.
Way out on the left wing and just over the halfway line, he gambled on a long punt at goal, catching keeper Steve Phillips off his line.
It did, with the hapless Phillips desperately trying to get a hand on the ball as it swept over his head.
Kelly, who had come up through the Rushden ranks, wasn't far off a second goal when his keeper Paul Bastock sent him away with the ball slung into the centre circle.
No-one got in a tackle as Kelly raced through to draw a full-length save from Phillips.
With both Simeon Jackson and Andy Burgess forcing saves, Rushden were well on top but all that changed just after the half hour.
Referee Paul Melin had decided, only an hour before the start, the tie could go ahead and he must have been close to ordering a halt as the intense storm broke.
Rovers were happy he didn't as Rickie Lambert set up Andy Williams for the equaliser and then Craig Disley worked a one-two with Sammy Igoe before running the ball past Bastock.
Rushden didn't deserve to be a goal down at the break but, within ten minutes of the re-start, it was all over.
Their defence, which had hardly been under any pressure, was suddenly porous.
They allowed Craig Hinton in for a free header at the far post and, a few minutes later, Lambert blasted an angled right-footed shot home.
There was a second goal for Lambert near the end when his captain, Stuart Campbell, put him in the clear.