After two victories the bottom club came up against the leaders and the gulf in class was there for all to see with Giuliano Grazioli grabbing a brace to take his season's total to 24.
Leigh's problems mounted with the sending off of Ryan Clarke in injury time for a second yellow.
Barnet, always in control, started brightly with Nick Bailey orchestrating them from midfield.
And it was one of his free-kicks that got Barnet going in the 13th minute and Leigh goalkeeper Jon Worsnop did well to turn it round the post.
Bailey was again at the hub of another Barnet move when he picked out Ismail Yakubu but the rampaging full-back headed straight at Worsnop.
Mark Peers tried his luck from 30 yards as RMI stuttered into the game, but his shot was well wide.
Worsnop then had to race from his line to dive at the feet of Ben Strevens after a cross from Liam Hatch caused problems in the home box.
It was no surprise when Barnet took the lead in the 37th minute following a great run by Dean Sinclair. He won a corner that Bailey played a short to Richard Graham and Grazioli headed past Worsnop.
Ryan Clarke was booked for a foul on Bailey six minutes after the break before Peers received the same treatment for another foul and from Bailey's free-kick, Strevens headed back into the danger area and Hatch beat Worsnop from close range.
Neil Gibson provided RMI's first goal attempt in the second half but was well off target from 25 yards.
Grazioli then latched on to a long clearance, but his lob on the turn was yards over the bar.
However, he did grab his second in the 77th minute when he showed his class to bring down a pass from Anthony Charles, beat his marker, and pass it into Worsnop's bottom left hand corner.
In a rare home attack Yakubu came to his side's rescue when he headed behind Peers' dangerous cross.
In the last minute Clarke cleared off the line to deny Grazioli a hat-trick and that was it for the Leigh defender, as a minute later he received his second yellow for a foul on Grazioli.