Leonard drew 2004 winner and last year's runner-up Mark Bemowski for Wednesday's third-round matchup. Bemowski toppled Ronald Richard, 2 and 1 in the second round at Victoria National Golf Club.
After Monday's opening round was washed out, the first round was completed on Tuesday. They also got through the second round and on Wednesday, there will be both the third round and quarterfinals.
Thursday will feature both the semifinals and final.
The other stroke-play co-medalist, Paul Simson, knocked off Richard Stevens, 4 and 2 on Tuesday. Simson will face Rick Woulfe, a 3-and-1 winner over Michael Puls, in the third round.
David Rasley beat Allan Small 2 and 1 to set up a third-round match against Tracy Scott, who advanced thanks to a 3-and-2 victory over Arthur Mielke on Tuesday.
Robert Mielcarz dispatched Greg Reynolds to the tune of 3 and 2. Mielcarz will now meet Kenneth Forster on Wednesday after Forster beat Alan Foster 4 and 2.
Tom McGraw bested Randy Reifers, 3 and 1 and will battle Gary Vanier on Wednesday. Vanier defeated Steve Dallas, 3 and 2 in Tuesday's second-round action.
Terry Tessary forfeited his match against Mike Bell, setting up a third-round match for Bell against Paul Schlachter, who moved on with a 2-and-1 win over Richard Thoms.
Sam Farlow beat David Stanfield, 3 and 2 and faces David Strawn on Wednesday. Strawn throttled Martin West, 6 and 5 on Tuesday.
Jerry Greenbaum came from behind to eliminate Joe Keller, 2 and 1. Greenbaum will tackle Erik Myrmo in the third round after Myrmo got rid of Doug Crawford, 3 and 2.