Clarets striker Austin opened the scoring in the second minute with his third goal in four appearances so far this term.
Yet Cardiff hit back five minutes before the break when Robert Earnshaw fired home an equaliser and neither side could find a winner thereafter.
Burnley boss Eddie Howe made three changes to his side following the Clarets' 2-0 Championship defeat at Crystal Palace last weekend.
Michael Duff started his first game of the season, replacing Andre Amougou, Dean Marney was restored to midfield and Austin was handed a starting role up front.
Striker Zavon Hines was named among the substitutes following his move from West Ham on Friday.
Cardiff boss Malky Mackay kept faith with the same side that lost 3-1 at home to Brighton in midweek.
And it was Burnley who began the brighter, tearing out of the blocks to open the scoring inside the second minute.
Defender Kieran Trippier engineered the space to flight a teasing cross into the heart of the Bluebirds' penalty box and Austin arrived to head home from six yards out.
The visitors gradually steadied themselves and almost drew an immediate response when Mark Hudson arrived to meet a cross, only to see his close-range header flash narrowly wide.
Yet Burnley almost doubled their advantage in the 11th minute when Trippier again found space down the flank and delivered another fine cross.
Austin was again there to meet his delivery but this time could only steer his header wide.
Clarets winger Ross Wallace then warmed Cardiff goalkeeper David Marshall's hands with a 20-yard strike before Jay Rodriguez headed wide midway through the first half.
Winger Keith Treacy flashed a 12-yard shot just wide in the 31st minute but the Bluebirds survived and drew level in the 40th minute.
Defender Andrew Taylor found Earnshaw with a neat pass and the former Nottingham Forest forward fired home a low left-foot shot from six yards.
Kenny Miller then saw a 20-yard shot blocked as the sides went in level at the break.
Chances came and went after the restart as Earnshaw headed goalwards from six yards in the 55th minute but Lee Grant made a comfortable save.
Four minutes later, Wallace spurned a decent opportunity when he hit a weak shot when well placed on the edge of the six-yard box.
In the 64th minute, Hines came on for Austin as Howe sought to breath new life into his attack.
Treacy went close for Burnley with a 12-yard strike that Hudson blocked and Hines went close twice in quick succession, first seeing a shot blocked by Hudson and then Kevin McNaughton as the sides remained on level terms at the final whistle.