Aaron Wilford nearly made it two when he just failed to get onto a cross from Chris Hughes. But unlike last season when United may have floundered, they got straight back into the game with youngster Andy Keogh equalising and they then started to dominate from then on.
Keogh charged down Michael Price's clearance and coolly slotted home from a tight angle.
The impressive Convery nearly put Darlington back into the lead but his low drive was saved by Leeds' Aussie trialist goalkeeper Adam Federici.
Polish trialist Tomas Rzasa's 25-yarder put The Whites into a 2-1 lead. Price could do nothing but grasp thin air as the shot flew past him. Jamie McMaster then headed Leeds' third when Price failed to judge the flight of the ball.
The home side pulled a goal back when Craig Liddle got on the end of a free-kick, heading home without any noteworthy challenge.
The defence had switched off again, which would be of concern to the Leeds backroom staff.
However, United seemed to be able to move up a gear when they wanted and McMaster notched his second and Leeds' fourth of the night.
A decent result, and a performance that showed some promise.
Rzasa was delighted with his own personal performance and he is due to find out in the next few days if he will be offered a deal at Elland Road. Chris Bart-Williams also showed some good touches on his debut, but Steve Guppy and Craig Hignett had a quiet game and it remains to be seen if they are offered deals.