The Scottish Premier League side took the lead seconds before half-time with a superb Tam McManus effort.
But United came back in fine style after the break and Ricketts equalised with a close-range header.
Frazer Richardson gave The Whites the lead with a deflected effort before Ricketts sealed the win with a simple tap-in.
The first real chance did not arrive until the 16th minute when Leeds should have taken the lead, but Julian Joachim's drive from 16-yards was saved by Simon Brown.
Brown saved Hibs again 10 minutes before the break, this time keeping out Brian Deane's drive from just 14-yards out.
Hibs' opener was superb. David Murphy fed Stephen Glass, who laid the ball off to McManus and he curled an angled shot from 16-yards past Leeds' debutant
keeper Neil Sullivan and into the net off the post.
Leeds drew level just after the hour mark when Ricketts, who had struck the crossbar seconds earlier with a shot, headed home from substitute Richardson's cross from the right.
Four minutes later Richardson gave Leeds the lead with a deflected shot from outside the box that looped over Brown and into the net.
Leeds were well on top now and in the 75th minute Ricketts was left with an easy tap-in after good work on the right by inspired 53rd minute substitute Richardson.
It could have been far more emphatic had Danny Cadamarteri found the time to shoot inside the area when he broke clear, but 3-1 was the perfect scoreline to end the pre-season for United.
"I thought Hibs looked well organised, they had a physical edge to them, they moved the ball about well," Kevin Blackwell said after the game.
"Neil Sullivan might not have had loads of saves to make but Hibs stretched us at times and, as the manager of the opposition, that's the sort of test you're looking for."
Hibernian: Simon Brown, Steven Whittaker, David Murphy, Gary Caldwell, Colin Murdock, Guillaume Beuzelin, Scott Brown, Grant Brebner, Gary O'Connor, Tom McManus, Stephen Glass.
Subs: Alistair Brown, Gary Smith, Derek Riordan, Kevin Nicol, Kevin McDonald, Steven Dobbie, Alen Orman.
Leeds United: Neil Sullivan, Gary Kelly, Matthew Kilgallon (Cadamarteri), Simon Walton (Bart-Williams), Michael Duberry (Carlisle), Paul Butler (Radebe), Julian Joachim, Jermaine Wright, Brian Deane (McMaster), Michael Ricketts, (Keogh), Danny Pugh (Richardson).