But their celebrations were brought to halt by the assistant referee's flag. Ipswich referee Mike Thorpe had a lengthy discussion with his assistant but then ruled that the goal stood.
A few minutes later Watford's Bruce Dyer out-jumped the defence but saw his header bounce down and just elude his follow-up attempt.
Then when home defender Neil Cox nodded the ball through, Jay Demerit saw his attempt strike Steve Staunton on the line.
Watford bemoaned their luck but while they were doing so City broke at the other end and Jorgensen slipped the ball through to the supporting Michael Doyle who drilled in the third beyond keeper Richard Lee.
City had looked the more composed side against a Watford side short of experience and often guilty of naive play.
City took the lead after 14 minutes when Trevor Benjamin beat the offside trap to head past Lee after meeting a floated free-kick from man-of-the-match Stephen Hughes.
City enjoyed the edge but were unable to make their superior possession tell and Watford broke back after 31 minutes.
Jermaine Darlington fed the ball through to Danny Webber who spun around Adrian Williams and crossed for Dyer to score from close in.
Watford had City rocking when Webber pulled a goal back on 84 minutes after breaking on to a long ball down the middle and wrong-footing Scott Shearer with a mis-hit shot but the visitors held on for three vital points.