Paul Lambert felt the cup victory was a real triumph over adversity after defeating Newport County 2-1 on Monday night.
The Rovers had to suffer illness and injury before the game and then the sending off of Chris Brown ten minutes into what could have been a potential banana-skin after County captain Mark Byrne had cancelled out Ben Marshall's early penalty.
But a hugely professional second half display culminated in half-time sub Jordan Rhodes grabbing his tenth goal of the season to send Rovers through to a fourth round tie at Oxford United.
"We lose Kilgallon to a sickness bug just before the game, and then we lose Williamson to injury in the warm-up," said Lambert.
"Then after taking the lead we lose Chris Brown. I thought the referee was quite quick to get his card out, but I need to see it again.
"75 minutes is a long time to play with ten men, especially on a pitch that is not in the greatest of conditions. That made for a difficult game.
"But I thought we deserved to win it, the ten men were outstanding."
The introduction of Rhodes proved to be the catalyst for a much-improved showing in the second half, with Lambert feeling the result was fully deserved due to their improvement after the break.
He added: "We changed it at half-time and went two up top and I thought we were fantastic, I really did. I thought there was only one team that was going to win it in the second half and that was ourselves.
"We could have easily sat with 4-4-1 but we put another striker in there and it is a fantastic winning goal.
"It was a terrific cross from Tom and he makes a brilliant run across the face and everybody knows that is Jordan's trait in the penalty box so I'm delighted with him.
"It is the second time that we've been down here in less than a fortnight and our supporters were fantastic coming down that distance to watch us."
Ticket and travel arrangements for the fourth round tie at the Kassam Stadium will be confirmed as soon as possible.