Simon Dawkins fired Derby into an early lead but Leeds dominated the second half, resulting in Smith's goal while they also had two penalty claims rejected.
The Rams were already assured of finishing third and will meet sixth-placed Brighton over two legs in the play-off semi-finals.
McClaren resisted the temptation to field a substantially weakened side in advance of the play-offs, although Craig Bryson and Supporters' Club Player of the Year Jake Buxton were handed places on the bench.
Leeds could hardly have made a worse start, falling behind in the sixth minute.
With the defence in disarray, Patrick Bamford's pass found Jeff Hendrick. His close-in shot was blocked by goalkeeper Jack Butland, but former Tottenham striker Dawkins reacted quickly to stab home his fourth goal of the season.
Conor Sammon should have doubled the Rams' advantage five minutes later, but he fired wide of the near post after breaking clear.
Leeds needed to step up their game and Lee Grant's goal was put under siege as the Derby keeper pulled off saves from Smith, Scott Wootton and Michael Brown, with Ross McCormack also going close with an inventive lob.
Michael Tonge claimed Richard Keogh handled his 20-yard shot as the interval approached but referee James Linington refused to award a penalty, and Tonge's luck was out again a minute after the break when his angled drive veered inches outside the far post.
Leeds, who replaced Luke Murphy with Aidy White at the start of the second half, saw their improvement rewarded with a 50th-minute equaliser.
McCormack broke down the left and timed his pass perfectly to Smith, who drew Grant off his line before clipping the ball into the far corner for his 13th goal of the campaign.
Leeds had their second penalty claim rejected two minutes later as Smith appeared to be impeded while running through the 18-yard box.
Derby had posed little threat going forward since their bright opening, but Hendrick thrilled the travelling support with a 30-yard drive which fizzed only just too high.
McCormack was denied his 30th goal of the season when Grant punched away the Scot's vicious free-kick from the edge of the box as Leeds continued to monopolise possession, and the unmarked McCormack then headed straight at Grant from Danny Pugh's precise cross.
Derby, who had won their last 10 matches against Leeds, settled back on defence for long periods and will need to show a more positive approach if they are to build a lead to take into the home leg of their play-off against Brighton.