Sandaza came on after 64 minutes to cancel out Hartley's opener
Francisco Sandaza was the Dundee United hero after the substitute scored the equaliser in a thrilling draw with reigning SPL champions Celtic.
United had earlier been angered when denied a penalty after Roy O'Donovan was challenged by Gary Caldwell.
That had come moments after Paul Hartley gave Celtic the lead with a low deflected drive just after the break.
United's Margaro Gomis came close to a winner, while Celtic's Scott McDonald missed from four yards out.
It means that Celtic, who beat St Mirren last weekend with a controversial penalty, have still not lost to United since 1999.
United had gone into the game still reeling from Monday's 3-1 mauling by Scottish Premier League newboys Hamilton Accies.
Angry manager Craig Levein dropped Darren Dods and Shaun Dillon and replaced them with Garry Kenneth and Mihael Kovacevic.
But the reconstructed defence would not have welcomed the news of the return of Shunsuke Nakamura, the Celtic midfielder being pressed into early action after his recovery from injury in place of virus-hit Barry Robson.
Nakamura was soon delivering some trademark crosses into the box, but United's tall defence coped well, rarely allowing the reigning champions a clear sight at goal.
And it was the home side, who failed to score against Celtic last season, that created the better chances of a hectic first half.
David Robertson, who had started in place of the off-form Prince Buaben in United's midfield, climbed to meet a Kovacevic cross, but Artur Boruc stretched to tip the ball over the bar for a corner.
The game threatened to boil over when United striker O'Donovan, their loan signing from Sunderland, was booked for recklessly hacking at Boruc as the goalkeeper shepherded the ball out for a goal kick.
And Celtic's Jan Vennegoor of Hesselink held down Lee Wilkie inside the visitors' box with what resembled a bear hug.
United left-back Danny Grainger drove a powerful volley over the crossbar from 16 yards before Celtic finally forced Lukasz Zaluska into a save after 39 minutes.
Aiden McGeady, already booked for a foul on Kovacevic, almost caught out the goalkeeper with a stinging long-range drive that the Pole palmed clear.
The visitors took the lead five minutes after the break when Mark Wilson, who had come into the side to replace the injured Lee Naylor at left-back, whipped in a cross to the back post.
Hartley (second right) put Celtic ahead at Tannadice
Nakamura took his time to pick out Hartley, whose low drive from the edge of the box nestled into the far corner via a deflection off Kenneth.
United ought to have had a penalty four minutes later when O'Donovan appeared to be felled as he tricked his way past Caldwell in the penalty box.
The home side were furious not to be given the decision by referee Charlie Richmond, who moments later was booed off the park after picking up an injury following a collision with Nakamura.
While Richmond was replaced with Iain Brines, Nakamura picked himself up to fire a powerful 20-yard volley straight at Zaluska.
Warren Feeney had a chance to make his mark seconds before being replaced by Sandaza but shot into Boruc's arms from just inside the penalty box.
It was Celtic's turn to squander a chance when McGeady and McDonald combined to send Vennegoor of Hesselink clear, but the Dutch striker's low drive struck the legs of goalkeeper Zaluska and bounced clear.
McDonald sent a shot on the turn over the bar, while O'Donovan should have done better than fire against Boruc when he stole clear behind the Celtic defence.
But United, who also had two claims for handball in the penalty box turned down, finally got the breakthrough when Craig Conway's low cross to the far post was turned home by fellow substitute Sandaza.
Gomis sent a powerful drive just over the crossbar, while McDonald headed wide from close range as both sides came close to a winner.
Dundee Utd: Zaluska, Kovacevic, Kenneth, Wilkie, Grainger, Flood (Conway 78), Scott Robertson, Gomis, David Robertson (Buaben 64), Feeney (Sandaza 64), O'Donovan.
Subs Not Used: McGovern, Dillon, Daly, McCord.
Goals: Sandaza 79.
Celtic: Boruc, Hinkel, McManus, Caldwell, Wilson, Nakamura (Robson 68), Hartley, Scott Brown, McGeady, McDonald (Samaras 88), Vennegoor of Hesselink.
Subs Not Used: Mark Brown, Crosas, Donati, O'Dea, Caddis.
Goals: Hartley 51.
Ref: C Richmond
BBC Sport Player Rater man of the match: Dundee United's Francisco Sandaza 8.28 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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