Christopher Schindler scored his first Premier League goal to earn Huddersfield just their third point of the season at Burnley.
The Clarets were looking for their third victory in a row and took the lead in the 20th minute through Sam Vokes, who could face retrospective action from the Football Association for an elbow on Schindler.
Huddersfield had only scored three goals in their seven previous games and from more than 70 per cent possession in the first half they managed 10 shots, none of which were on target.
But they kept pushing in the second half and got their reward in the 66th minute when Schindler headed the equaliser, with the 1-1 draw enough to lift David Wagner's side off the bottom of the table.
Both teams had good news on the injury front, with Schindler overcoming a knee injury and Burnley centre-back James Tarkowski recovering from a groin problem, which should mean he is clear for England duty.
Burnley had the best chance of the early stages when, with six minutes gone, Ashley Westwood sent over a fine cross that Vokes headed straight at Jonas Lossl.
That was not representative of the balance of play, though, with more of the action in the home penalty area, notably Jonathan Hogg's half-volley from a corner that flew just over the bar.
Ben Mee had Tarkowski to thank for bailing him out in the 15th minute. Mee gave the ball away to Aaron Mooy in the area and he squared for Laurent Depoitre, who looked odds on to score only for Tarkowski to pull off a last-ditch block.
And five minutes later, Vokes made no mistake with his second chance, scoring the first goal between the sides in the Premier League after two goalless draws last season.
In-form winger Johann Berg Gudmundsson sent over a cross from the right that saw Vokes rise and twist to direct a perfect header into the bottom corner for his third goal of the season.
Moments later the German was on the floor and needing lengthy treatment to a cut above his eye after taking first a naughty elbow from Vokes and then a shot in the face from Westwood. There was a significant amount of blood but Schindler was able to continue after a change of shirt.
The home fans were becoming frustrated by their team's failure to stamp any authority on the game and in the end were relieved to take a point after surviving eight minutes of injury time.
Huddersfield continued to be the more impressive side right up until the final shot. Rajiv van la Parra's 30th-minute effort was a perfect example, with excellent build-up play only for the Dutchman to curl the ball wide.
The pattern continued after the break, and it was not until the 57th minute that Hart was finally forced into a save, pushing aside Mooy's shot from the edge of the box.
Depoitre chased after the loose ball and went down appealing for a penalty but referee Christopher Kavanagh spotted that Tarkowski had not made contact and booked the Huddersfield striker.
That would have pleased Burnley boss Sean Dyche, who lamented this week an apparent relaxation in efforts to stamp out cheating.
It was Depoitre's last contribution as he was replaced by Isaac Mbenza while Steve Mounie came on for Van la Parra.
Burnley also made a change, Chris Wood coming on for Ashley Barnes, but they showed little interest in attacking and were finally punished as Schindler rose highest to head in Chris Lowe's cross.