Town, who were without a game on the Saturday, looked sharper all over the pitch and were not flattered by their 2-0 lead, courtesy of goals for Taylor Hamill and Scott Hennell.
However, a change of formation from Hibs’ player-coach Rich Kay heralded a turnaround in fortunes for the visitors.
Kay halved the deficit with a 25-yard strike before Calum Yeates calmly converted a one- on-one to draw Hibs level.
Ollie Manuel then saved a last-minute penalty to prevent Town regaining their lead.
After a disappointing 3-0 home defeat at the hands of Coventry United on the Saturday, Kay was delighted with the fight shown by his side.
“We looked tired which is to be expected with two games in three days and both being local derbies,” said Kay.
“But it’s pleasing that from 2-0 down we had the spirit and fight to get a point as there were some very tired legs.”
Kay blamed both concessions on a hastily put together defence, but reserved special praise for Nathan Neale, who returned to the side despite not being fully fit.
“We are decimated with injuries so it was very much a makeshift back four and the two goals we conceded came from that.
“Nathan put his body on the line to play and help us get a grip of the game and he was outstanding half-fit.
“I can’t wait for things to settle down and get our best defenders fit and firing because we need our best players on the pitch, like any team.”
The former Southam midfielder was far from impressed with the performance against United, however.
Daniel Stokes scored twice to take his tally to seven goals in two games against Hibs, with Brian Ndlovu also on target for the Coventry outfit.
“We again started slowly and conceded a sloppy goal but I was more disappointed with our attacking reaction,” admitted Kay.
“We passed the ball poorly and that helped them get a grip of the game.
“We defended well for the most part but we conceded again one minute before halftime to go in two-nil down and with a mountain to climb.”
Hibs entertain Polesworth tomorrow in the league, while Kenilworth play hosts to Badsey in the Challenge Vase before a home Division Two clash with Alcester on Tuesday evening.