IS there a team out there more delighted to see the back of 2015 than Dundee United? At the bells last year, the Tannadice side were spanking their Dundonian rivals 6-2 and speaking dreamily of winning the treble. Instead the sales of Stuart Armstrong, Gary Mackay Steven and Nadir Ciftci ripped the heart out of the team, and that victory was one of just eight league wins in the entire calendar year, leaving them ten points adrift at the bottom of the Ladbrokes Premiership.

The latest sorry chapter in this tale of woe unfolded at Tynecastle last night, with the club's inability to keep goals out of their net exposed for all to see. Not only did they concede another three, they must now face their city rivals in the New Year derby without first choice defenders Callum Morris, who was stretchered off with a medial ligament injury, and Mark Durnan, who was sent off last night but was suspended anyway.

Things haven't got worse since Mixu Paatelainen took over from Jackie McNamara but they haven't got much better either. In eleven matches in charge, the Finn has now won one and drawn two and at points seemed to be approaching the end of his tether.

"The goals we conceded were a joke again," said Paatelainen. "Obviously the goal the goalkeeper parries into his own net, we need to avoid goals like that. The effort the boys showed was excellent, the organisation a man down was excellent. But if we defend sloppily against Dundee they will punish us."

He went with an unchanged side from the one which lost an injury time equaliser at Inverness last time out, which meant no sign of Eiji Kawashima, the club's new Japanese goalkeeper, who is back home as his pregnant wife prepares to give birth. Robbie Neilson made three changes to the side which drew against Celtic on Sunday, with club captain Alim Ozturk making his first appearance since September as he works his way back from the two hernia operations he has undergone since leading the Tynecastle side to the Championship title.

Their win means they are now seven points back on both Aberdeen and Celtic at the top of the table. "It was a great night for us," said Neilson. "St Johnstone got beat and Aberdeen drew and that lifts us up the league a wee bit, a wee bit closer to Aberdeen and a wee bit further away from St Johnstone."

Kawashima's unavailability meant Michal Szromnik started between the sticks and from the moment he strolled out his box to chest down a clearance, presented the ball to Osman Sow and required to be bailed out by Callum Morris, this was to be a difficult evening for the Pole.

United actually had an early lead, referee Bobby Madden pointing to the spot when Juwon Oshaniwa rashly slid in, making enough contact to allow Scott Fraser to tumble to the ground. Billy McKay sent Neil Alexander the wrong way from the spot.

The visitors had a platform to build but as usual the foundations were hardly solid. With Billy King, Sam Nicholson and Gavin Reilly in lively mood, Szromnik needlessly conceded a corner and Reilly reacted well to volley the equaliser after Igor Rossi had flicked on King's delivery.

Paatelainen booted the advertising hoardings with fury when a combination of a weak Demel clearance and some further hapless goalkeeping from Szromnik gave Hearts the lead via a swerving Prince Buaben strike and it was three before the half hour. Morris misjudged his lunge on the pacy King inside the box and Sow converted the penalty.

Some shoddy defending at the other end this time gave United a route back into the match, Fraser's free kick missed by everyone and ending up in the net, but even then the visitors contrived to throw their momentum away. Seconds later Reilly had the run on Durnan, who hauled him back and was dismissed.

Paatelainen sacrificed McKay to make up for the numerical shortfall, with the game plan to keep the match alive until the closing stages. This they duly did, even if the second half was one-way traffic. Efforts from substitute Arnoud Djoum and Reilly allowed Szromnik to partially redeem himself, while Reilly blotted his copy book by spurning two one-on-one chances. Djoum, King and Nicholson might have made things easier, but contract rebel John Souttar was unable to turn the jeers into cheers when he arrived as a late throw of the dice. So United's 2015 ends in defeat. At this rate their 2016 might be a lot worse.

Hearts 3

Reilly 18, Buaben 27, Sow 30 pen

Dundee United 2

McKay 2 pen, Fraser 44

Hearts (4-4-2): Alexander; McGhee, Ozturk, Rossi, Oshaniwa; King, Buaben, Gomis (Djoum 45), Nicholson (Zanatta 83); Sow (Swanson 80), Reilly.

Subs not used: Hamilton, Augustyn, Pallardo, Buchanan

Dundee United (3-4-1-2): Szromnik; Durnan, Morris (Dillon 45), Gunning; McGowan, Demel (Souttar 80), Rankin, Dixon; Fraser, Erskine; McKay (Spittal 45).

Subs not used: Zwick, Murray, Spark, Bodul

Booked: Hearts: Gomis 34. Dundee United: Dixon 80.

Attendance: 16,721

Referee: B Madden