North End captain Clarke bundled home a header from inside the six-yard box in the 90th minute for what was the only goal of a poor-quality affair.
The result lifts Alex Neil’s side to within a point and a place of the play-off spots but for fellow promotion chasers Cardiff, who remained third in the table, it was another underwhelming display.
Preston had the better of the chances and just edged the encounter as they got their rewards for some attacking endeavour in the game’s final quarter.
The visitors went into the game in the Welsh capital unbeaten since November 4 and started well. In their change yellow strip, Daryl Horgan had the game’s first chance, but could not find the target as a wild left-footed effort sailed wide.
Both teams struggled to get going in an uneventful first half, but it was Preston who were both marginally better on the ball and created the better opportunities.
Paul Gallagher – on his 450th Football League appearance – put a free-kick into the home wall and Alan Browne shot wide as referee James Linington proved unpopular with the Cardiff crowd.
The Bluebirds did finally get up a head of steam just before the break, Kenneth Zohore seeing a shot blocked while Lee Tomlin lacked the pace to make the most of a rare home counter-attack.
Gallagher’s woeful free-kick before the break summed up the opening 45 minutes as the teams turned around with nothing to separate them.
The second half was not much better initially. Tomlin had a flicked header saved by Chris Maxwell while at the other end, Horgan’s neat turn saw him run into space but shoot over from 25 yards.
Home boss Warnock had seen enough and introduced Junior Hoilett for the anonymous Liam Feeney in search of a goal.
Preston made a double change too, Neil gambling with the introduction of Josh Harrop and Callum Robinson as the visitors continued to look dangerous on the counter.
North End continued to press, and only a superb diving tackle from Cardiff centre-half Bruno Manga denied striker Jordan Hugill what would have been a simple tap-in.
Manga then went close with a header at the other end, but there was still time for a late breakthrough.
Cardiff had looked vulnerable from set-pieces and they were made to pay as the ball fell the way of Clarke and he did the rest to score the game’s only goal.