The German wing-back terrorised Rovers' right-hand side - he scored the vital first goal, created the second, was inches wide with a 20-yarder and set up gilt-edged chances for Teddy Sheringham and Les Ferdinand.
Out for a month with knee trouble, Ziege, who joined the German squad last week, was back in the starting line-up to devastating effect.
It took just eight minutes for Ziege to strike. Ferdinand initially lost the ball but won it back, Sheringham passed it on to Davies who magnificently spotted Ziege's run and found it with a volleyed pass. Ziege settled himself before lashing past Achterberg from 10 yards.
Ziege found space as Ferdinand switched play and the striker then picked up his cross, turned on a sixpence but somewhat scuffed his shot wide from 15 yards.
Poyet's speculative volley from 30 yards was saved athletically by Achterberg and with 21 minutes on the clock Ziege picked up the loose ball after Ferdinand and Sheringham had probed on the edge of the area and curled inches wide with his right foot.
Taricco forced another hurried save from Achterberg as we broke from a Rovers attack after 23 minutes but danger minutes later as Hill met Navarro's corner perfectly from 10 yards only for it to hit his own player.
Ziege was at the hub again on the half-hour, crossing low only for Sheringham to miss the target from close range.
It was only a matter of time before the second goal and, once again, it came via Ziege.
This time Sheringham drilled a pass out wide, Ziege crossed first time and Poyet clipped home a delightful left foot shot from 12 yards.
It took Poyet into double-figures for the season having, ironically, opened his account in the 4-0 Worthington Cup win against Rovers back in October.
We enjoyed plenty of possession at the start of the second half without really creating a chance before Rovers hit back with their best spell.
Henry fluffed the best chance, mis-hitting his shot from only 10 yards, after 57 minutes and a minute later former FA Cup winner Rideout dragged his shot wide from 15 yards.
The third goal was always going to be vital and it arrived just after the hour.
Sherwood crossed from the right, Ferdinand challenged Achterberg and Sheringham planted the loose ball in the bottom corner.
Ziege was now in acres of space down the left flank and another superb cross, fizzed in across goal, found Sheringham at the far post but the skipper failed to connect properly and it bounced to safety.
Taricco and a deft Davies flick carved out the next chance for Sheringham after 79 minutes but this time Allen's last-ditch tackle took teh sting out of the effort.
Rovers continued to press as Barlow's shot was fumbled by Sullivan but our Scottish number one was up on his feet to block Price's close-range rebound, Sullivan the saved low from Koumas and Barlow missed the target from six yards when he should have done better.
But the last word went to Poyet. Sheringham, on the left, found him with a precision pass and the Uruguayan's shot deflected off Hill beyond Achterberg. A little harsh on Rovers perhaps, but the perfect prelude to the big one at Cardiff next week.
Christian Ziege marked his return from injury with an inspirational first half display to help book our place in the last eight of the FA Cup.