Hyundai driver Paddon inherits a lead of just over a half a minute, and has four stages to hold on ahead of reigning champion Sebastien Ogier.
Latvala has never won consecutive WRC rounds, and held a 14.5s lead before his crash, which Thierry Neuville described as "huge" after passing him on the stage.
Television crews working on the stage reported that Latvala and co-driver Miikka Anttila were unhurt.
Latvala continues to lead in Argentina
Latvala produced a comfortable and well-managed victory on Rally Mexico last time out, and looked set to do the same again before the incident on the penultimate stage of Saturday's leg.
Paddon came close to victory on Rally Italy last year where he led until he hit a rock, causing transmission damage.
Hyundai has one WRC win courtesy of Neuville on Rally Germany in 2014, but a triumph in Argentina this weekend would be the first for the current-spec i20 introduced in Monte Carlo this year.
Though Paddon still has to fend off Ogier, the Frenchman has struggled with sweeping the road in Argentina - which remains the only current WRC round he has not yet won.
Latvala maintains slender Argentina lead
Latvala holds narrow Argentina advantage