The Terriers were well on top at Turf Moor, yet they looked destined for defeat through Sam Vokes's first-half header before Christopher Schindler responded midway through the second period.
Wagner's men had enough chances to win this game against hosts who looked out-of-sorts, but the lack of a clinical front man let them down as it has so often this term.
An away point represents a reasonable return, but Huddersfield must start winning games soon or risk being cut adrift in the relegation zone.
Huddersfield started brightly but its profligacy cost it as Jonathan Hogg fizzed a big chance just over and James Tarkowski blocked from Laurent Depoitre prior to Burnley's opener.
Vokes towered a header past Jonas Lossl from Johann Berg Gudmundsson's centre, before the earlier pattern of play was reprised and Rajiv van La Parra sent a wild effort wide after breaking free on the left side of the area.
Joe Hart was not worked until just before the hour mark when an Aaron Mooy drive brought a clumsy save, and Vokes then came close to doubling Burnley's lead with a close-range flick from Gudmundsson's scuffed shot.
Huddersfield finally forged its breakthrough shortly afterwards, scoring in a similar manner to Vokes's earlier strike. Schindler attacked Chris Lowe's delivery and powered a header beyond Hart to clinch a share of the spoils.
Burnley will have time to regroup during the coming international break before taking on a tough run that begins with a trip to Manchester City.
Huddersfield's fixture list is no kinder, with Liverpool up next.