Town responded to the call by taking a two-goal lead against Carlisle but they could not move into second place as the Cumbrians fought back for a point.
Huddersfield and Carlisle are due to face each other three more times in the next few weeks and if this game is anything to go by fans are in for some exciting football.
Town will be hopeful that they can get back to winning ways before that starting with a victory over Sheffield Wednesday today.
Things started well enough for Huddersfield when captain Peter Clarke led by example to fire them into a 23rd-minute lead. Lee Novak's header was saved by Adam Collin but the former Gretna man was quick to slip the rebound to Clarke to slot home.
Town needed the woodwork to stop United making a quick reply. Ben Marshall tricked his way past two defenders to fire in a shot that came back off the foot of a post with Alex Smithies struggling.
Substitute Scot Arfield extended Town's lead when the ball fell kindly to him off defender James Chester and he swept it past Collin for a second goal that should have put Town in the driving seat.
But Carlisle were in no mood to capitulate. Francois Zoko gave them a lifeline with a 71st-minute header after Frank Simek's cross had been flicked on by Gary Madine.
Carlisle continued to press and with eight minutes left, Smithies did well to turn away former Town player James Berrett's header and then deny Madine but he could do nothing to stop Chester's powerful header to level the scores.
Manager Clark moaned: "To be two goals up away from home and with the clock ticking down... we've had a poor finish to the first half of the season.
"We defended too deep and couldn't get out of our box and allowed Carlisle to get crosses in for the lad Madine, who is a massive threat. "If we'd kept our shape in midfield we wouldn't have allowed Carlisle to come back at us," said Clark, who had given a rare start in central defence to Nathan Clarke.
"My players asked Huddersfield a lot of questions today," said Carlisle chief Greg Abbott.
Carlisle United: Collin; Simek, Chester, Michalek, Robson, Taiwo; Berrett, Marshall (Thirlwell 38), Curran (Bowman 79); Madine, Grella (Zoko 58). Unused substitutes: Caig, Murphy, Cruise, Hurst.
Huddersfield Town: Smithies; Peltier, P Clarke, N Clarke, T Clarke; Ridehalgh, Gudjonsson, Kilbane, Lee (Arfield 57); Novak, Afobe (Rhodes 73). Unused substitutes: Bennett, Roberts, Pilkington, Atkinson, Carey.
Referee: G Eltringham (Tyne & Wear).
Man of the match: Lee Novak.