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The League One struggler saw off Bristol City 1-0 in the rearranged tie, with Kiwi forward Waine finally breaking past the Championship side after 112 minutes.

City could not find a way back into the match, and as a result, Port Vale will now take on Premier League side Sunderland.

The original tie was due to be played on Valentine's Day, but had to be postponed because of a waterlogged pitch.

Despite sitting bottom of League One, Port Vale enjoyed the better chances in the first half, even if Bristol City dominated possession.

Home keeper, Australia international Joe Gauci, had to deal with some early pressure from a dangerous back pass, with the pitch conditions making any such passes particularly perilous.

Vale had the first real chance when Connor Hall fired a cross in from the left, but Waine's glancing header drifted wide.

Rhys Walters then had another sight at goal for the League One outfit, with a smart volley from the edge of the box, but it deflected off Waine and was comfortably stopped by Joe Lumley.

Sinclair Armstrong then got into a dangerous position for City, but his cutback was well dealt with by Hall and Jordan Gabriel.

Right on the stroke of half time, Vale had one final chance, with Waine again off-target after Gabriel had put the ball into the six-yard box.

After having much of the possession in the first half, the visitor from the Championship showed more intent in the second half with Sam Morsy particularly influential.

But while it was able to put Vale under pressure, the final ball often proved the issue, with the visitor regularly having to settle for corners rather than shots on target.

After Gerhard Struber had turned to his substitutes, Emil Riis almost set up a last-gasp winner but Sam Bell's desperate attempt to divert it home only resulted in another corner thanks to a late Jaheim Headley intervention.

With neither side able to find a winner in 90 minutes, the tie went into extra-time and the Robins were grateful to Cam Pring who did brilliantly to deny Waine, clearing the Vale striker's effort off the line.

At the other end Gauci did brilliantly at the start of the second half of extra-time to keep out a Tomi Horvat free-kick, diving to his left to deny the Slovenian.

That proved costly when Waine finally broke the deadlock. Taking advantage after City had failed to deal with Andre Gray's clearance, Waine rounded Lumley and steered the ball home.

City had one final chance to level, but Mark Sykes put a brilliant chance wide when he looked certain to score from a couple of yards out.