Hull started to come back into the game and on 19 minutes good football by the Tigers led to a Ryan France cross with Craig Fagan getting on the end of it, but he couldn't get enough on it as it was easily collected by Reading keeper Marcus Hahnemann.
Taylor's men kept on battling and on 26 minutes Kevin Ellison showed great determination to break into the box but couldn't find the final touch as he smashed the ball into the sidenetting.
On 30 minutes Reading countered again with great pace, but Hull defended well as John Welsh and Damien Delaney combined well to clear the ball successfully.
Reading went on the attack again as on 35 minutes a Chris Makin put in a terrific cross, but as Doyle rose to the header it was stopped by a superb save from Myhill.
In the second half Hull continued to battle on and their efforts paid off on 55 minutes as a corner from Curtis Woodhouse was met with a towering header from Leon Cort who smashed the ball against the crossbar.
The rebound fell back to Woodhouse who put in another cross, with loanee Chris Brown getting on the end of it inside the six-yard box and to the delight of the home fans he slotted the ball past Hahnemann to put the Tigers 1-0 up.
Reading were eager to get back on level terms and managed to do so in the 74th minute as a pinpoint cross from Nicholas Shorey from the edge of the area saw Glen Little rise above the City defence and head neatly into Myhill's bottom right-hand corner.
Reading pushed on and nearly claimed all three points in the 90th minute as another accurate Shorey cross left Brynjar Gunnarsson with a great chance, but he glanced his header wide past Myhill's left-hand post.