Leading 2-1 thanks to a Robbie Fowler brace in the 28th and 61st minutes the Bluebrds were pinned back when Preston were awarded a free-kick.
Davidson thumped home his second goal of the game having also netted in the 51st minute.
City made two changes following the midweek defeat to Watford with Ross Turnbull and Chris Gunter making way for Michael Oakes to make his debut in goal and Joe Ledley.
A superb save by Preston keeper Andy Lonergan prevented the Bluebirds taking a 15th-minute lead. The ball was swiftly brought out of defence to Paul Parry whose deep cross was headed goalwards by Ledley only for Lonergan to leap across and brilliantly tip the ball over the bar.
Cardiff deservedly took the lead when Fowler met a Ledley cross and powered a header into the back of the net.
Gunter replaced Parry for the start of the second half but Preston immediately went on the attack and six minutes into the half they equalised when a poor clearance header by Roger Johnson fell to Davidson and his shot through a crowded penalty area beat the diving Oakes.
Back came City and just after the hour they were back in front when Fowler went in bravely and headed his second from Ledley's corner.
Ledley went close with a header from a Gunter cross as the Bluebirds went looking for a decisive third goal but the visitors looked dangerous every time they worked their way deep into the City half.
They equalised in the first minute of stoppage time when a well-worked free-kick fell to Davidson and he powered a left-foot drive into the corner of the net.
Straight after the goal Johnson was stretchered off the pitch with his leg in a splint.
It was a disappointing way for the Bluebirds to end yet another game that they should have won.
External Reports
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