Leeds had dominated possession for the majority of the game but having established a 12-6 lead they were guilty of dropping off and allowing winger Mark McCrea in for a try which was converted by Paul Steinmetz to claim victory.
Stuart Lancaster took his side across the Irish Sea to take on former European Champions Ulster at Ravenhill in Belfast for their second pre-season game.
The wins over Doncaster at first team and development team level last Sunday gave Leeds fans plenty of confidence but Lancaster knew his side were in for a tough challenge.
Ulster had the visitors on the back foot in the early exchanges as they looked to take full advantage of the windy, slippery conditions. However, good work by Jon Goodridge and Alberto Di Bernardo cleared the pressure.
The Leeds forwards showed great strength to move up field and eventually the pressure told as referee George Clancy gave a penalty to Leeds 25 metres out for interference at the ruck. Di Bernardo struck the penalty cleanly to make it 3-0 after five minutes.
The Leeds forwards continued to assert their dominance and put the Ulster pack under real pressure. The man organising that show of power was Joe Bedford who was at the heart of everything good for Leeds.
Eventually the visitors got the chance to extend their lead when Richard Welding did well to hold on to the ball after being met by strong defence from the home side. However, referee Clancy saw a Ulster hand in the ruck and awarded Leeds a penalty on the 40 metre line. Di Bernardo hit the ball firmly into the breeze to double the lead to 6-0 after 15 minutes.
Ulster halved that lead after 21 minutes when Leeds withstood heavy pressure from the home side but they were penalised after a scrum collapsed 10 metres out. Niall O'Connor added the easy penalty to make it 6-3 after 21 minutes.
Leeds showed great composure to hit straight back after 25 minutes and once again it was Di Bernardo who kicked the points after Leeds were awarded a penalty 24 metres out.
As the game ebbed and flowed, Ulster hit back themselves two minutes later as the referee penalised Leeds for holding on and O'Connor had another straight forward penalty chance to make it 9-6 at half time.
After the restart Leeds dominated the first ten minutes of the half. They were awarded four penalties on the Ulster line after a succession of offences by the home pack on their own line. If this had not have been a pre-season match, a penalty try would have been expected however Leeds were left frustrated as the home side eventually managed to clear their lines.
Ulster were reduced to 14 men after 55 minutes when second row Ryan Caldwell was sin binned for a late tackle spotted by the touch judge. Leeds looked to turn the screw and once again camped on the Ulster line but they were unable to cross and the home side eventually managed to counter attack as the early drizzle turned into heavy rain.
The home side got their tails up with that attack and had their best spell of pressure in the game and it took some stout defending from the visitors to keep their line intact.
The Leeds lead was extended after 68 minutes when Di Bernardo struck an audacious drop goal from 43 metres out to make it 12-6.
However, Leeds were hit with a sucker punch three minutes later when Mark McRea broke through the attempted tackle of Richard Welding and raced in for a try from 25 metres out. Paul Steinmetz kicked the conversion to give his side the narrowest of leads with time running out.
Leeds had the chance to snatch victory in the closing minutes when Alberto Di Bernardo had a penalty attempt from the touchline but his attempted drifted wide and the visitors lost out 13-12 in Belfast.
Ulster: Bartholomeusz, Keyttle, Cave, Steinmetz, McCrea, O'Connor, Campbell, Fitzpatrick, Brady, Court, Barker, Caldwell, Henry, McMillan, Wilson
Replacements: Carey, Philpott, Bowe, Paulo, McCullough, Anderson, Pollock, Marshall, Larkin, Mallon, Cunningham
Leeds: Goodridge, Hughes, Hepworth, Welding, Biggs, Di Bernardo, Bedford, Cusack, Rawlinson, Hopcroft, Hooper, Myall, Dunbar, Fourie, Oakley
Replacements: Noon, Parkes, Bouza, Lock, Edwards, Vasey, Blackett, Hinton
Referee: George Clancy