Svoboda carded a third-round 66, while MacKenzie shot a five-under-par 65 as the pair moved to 12 under in Georgia on Saturday.
Without a PGA Tour win to his name, Svoboda recovered from a double-bogey on the back nine to power up the leaderboard with three birdies at the Seaside Course in Sea Island.
Svoboda, who managed just one top-three finish last season, enjoyed a bogey-free front nine after sinking birdies at the first, eighth and ninth holes.
MacKenzie joined Svoboda at the summit after a topsy-turvy end to his third round.
The 40-year-old - searching for his third PGA Tour title and first since 2008 - made a spectacular start to the third day by shooting a hole-in-one from his 174-yard tee shot at the par-three sixth.
MacKenzie then exchanged a birdie and a bogey at the 16th and 17th holes before draining a 44-foot putt to ensure he ended the round level with Svoboda.
American Russell Henley is one shot back after posting a 68 on the penultimate day.
Henley held a one-shot lead overnight but a bogey at the 15th saw him drop two spots to 11 under through 54 holes.
A group of five players - headlined by Stewart Cink - are three shots off the pace in a tie for fourth approaching the final round.
Cink rose 37 positions thanks to his seven-under-par 63, which included eight birdies, with four of those coming in succession at the 12th hole through to the 15th.
The American is joined by countrymen Andrew Putnam (66) and Deutsche Bank Championship winner Chris Kirk (66), as well as Argentine Fabian Gomez (68) and Zimbabwe's Brendon de Jonge (69).
Ken Duke (66), Scott Piercy (68) and Mark Wilson (69) are a shot further back.