The Robins eased to a 5-1 win when these two sides met here in the FA Cup last month but their defence has taken a major hit in the past week with Rob Atkinson following Rob Dickie in being ruled out long-term - and Kjerrumgaard quickly found an early way through their reshuffled rearguard.
Giorgi Chakvetadze shook off Mark Sykes down the wing and picked out Edo Kayembe in the box - he passed straight to the Dane who scooped the ball up and over Vitek at the near post.
Bristol City immediately searched for an equaliser and Ross McCrorie's first-time volley forced a save out of Egil Selvik, while Jason Knight's calls for a penalty for handball were denied.
But Watford almost doubled their lead when Neto Borges brought down Nestory Irankunda and Goglichidze's header from the resulting free-kick hit the post, with a grateful Vitek pouncing on the loose ball.
It continued to be a lively first half as Tomi Horvat's shot from distance required a diving save from Selvik, while at the other end Irankunda almost made it 2-0 with a superb strike from range that curled just wide of the top corner.
But Bristol City levelled 10 minutes before the break as Twine - usually a direct free-kick expert - somewhat uncharacteristically nodded in Randell's cross.