The Canaries took the lead through a Zak Whitbread header in the 27th minute at the KC Stadium, but Barmby arrived at the near-post to level from close range midway through the second half.
The visitors are now just one point clear in second, while Hull kept alive their slim hopes of snatching a play-off place.
The Tigers made one change from the side which claimed a 1-0 win at Coventry last weekend, with Jack Hobbs replacing Tom Cairney.
Norwich also made one change to their starting line-up, with Henri Lansbury coming in for Simeon Jackson.
Inconsistent Hull, who had won three and lost two of their last five games before today, saw a goalbound effort from Liam Rosenior blocked by Elliott Ward in the early stages.
Tigers striker Aaron Mclean, who scored the only goal against the Sky Blues last Saturday, fired a shot inches wide from 20 yards in the 21st minute, but the visitors took the lead shortly afterwards.
A free-kick from David Fox caught out goalkeeper Brad Guzan and Whitbread was left with an easy header from 12 yards.
Lansbury cracked a shot over the crossbar from another quick break, but Hull responded well.
Matt Fryatt broke into the box and unleashed a low drive which was well saved by John Ruddy, and moments later James Harper was presented with a golden chance from four yards but somehow put his shot over the crossbar.
Goalkeeper Ruddy came to the rescue again in first-half stoppage-time, tipping over a 30-yard free-kick from Andy Dawson.
Hull continued to press at the start of the second half, with Mclean heading over from a Dawson set-piece, but the Canaries hit back with Fox heading wide from a Ward centre.
It could have been 2-0 to the visitors in the 59th minute when a fierce shot from Wes Hoolahan was superbly tipped away by Guzan at the near-post.
Norwich felt they should have had a penalty when Russ Martin was pulled to the ground by Dawson, but appeals were waved away by referee Rob Shoebridge.
Top scorer Grant Holt volleyed over from 20 yards as it looked like Paul Lambert's men would add a second.
But Hull snatched an equaliser in the 73rd minute when Fryatt broke down the left and sent the ball across the six-yard box for substitute Barmby to pounce.
The game was on a knife-edge as it entered the final quarter, with Anthony Gerrard heading a right-wing corner wide, while Corry Evans let fly from distance but Ruddy gathered.
Sub Simeon Jackson came close for Norwich with a curling effort, and Tijani Belaid had the best late chance but Ruddy kept out his fierce drive.
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