However, Hunt nodded in from close range to spread panic in a defence without a clean sheet all season and the Republic of Ireland international's cross-shot produced the equaliser 12 minutes from time.
Although Bolton have now taken six points from their last four matches for manager Gary Megson, who again fans called to be sacked, this was a huge missed opportunity.
Having been out-played for three quarters of the game Hull - who have not win at Bolton since March 1935 - will have been satisfied with a point as they had lost three of their last four league matches and are still to win away this season.
After 20 minutes of relatively nondescript action Bolton took the lead out of nowhere with a typical piece of route one football.
Zat Knight's high ball forward was knocked down by Lee Chung-Yong, under pressure from Andy Dawson, on the edge of the area and Klasnic took one touch before blasting a left-footed shot past Boaz Myhill, who appeared slow to get across his goal.
The goal was the on-loan Croatian's sixth in his last eight league matches.
Five minutes later Jussi Jaaskelainen fisted away Dawson's 25-yard free-kick and then had to be quick off his line to beat Jozy Altidore to Craig Fagan's through ball.
Hunt should have equalised in the 35th minute when Jaaskelainen fumbled a cross under pressure and the ball bounced off Gretar Steinsson to the Hull midfielder but his poorly directed close-range header glanced the Bolton defender and went for a corner.
Tamir Cohen's foul on Altidore gave Hull a 30-yard free-kick a minute before the interval but the USA international drove wide.
Seven minutes into the second half Kamil Zayatte reacted a fraction of a second quicker than Cohen to flick away Paul Robinson's hanging free-kick as the Bolton midfielder prepared to shoot from six yards.
But Wanderers' defence has had cracks in it all season and no more so was it evident on the hour when the unmarked Zayatte planted a header wide from Hunt's right-wing corner when he should have hit the target.
It was to prove a costly miss as Bolton went straight down the other end and added a second, for which Myhill was culpable.
The Hull goalkeeper came to collect Robinson's free-kick from the halfway line as it dropped gently into the penalty area but he failed to reach it as Davies out-muscled Bernard Mendy to nod a back-header past him.
Gary Cahill could have made the game safe but saw his low drive deflect enough off Anthony Gardner for Myhill to turn it around the post.
Bolton's hopes of a first clean sheet of the season were dashed in the 71st minute when their defensive frailty was exposed as Fagan crossed and Hunt out-jumped Steinsson to head home.
Seven minutes later the Tigers midfielder scored a fortuitous equaliser when Jaaskelainen could only get a fingertip to his cross-shot from Zayatte's punt to the far post and the ball crossed the line despite the best efforts of Robinson to hook it out
In the last minute Steinsson almost bagged the winner but his 18-yard shot was deflected just wide.