Song had a 10-foot putt on the 16th green to stay at 12-under-par, while Spieth was presiding over a five-foot birdie effort on the last to sign for an 11-under total when play was halted just before 3 p.m. (0700 GMT) because of inclement weather.
"Assuming I make that putt on 18 that is going to put some pressure on," Spieth told reporters after shooting four-under for his 17 holes.
"I was due to leave tonight but next week was an off week anyway so we have changed the travel schedule. It is what it is. I will come back tomorrow and try and win this thing."
China's Liang Wenchong was the leader in the clubhouse at 10-under after shooting a final round two-under 69 but he missed a short birdie effort on the last hole, 10 minutes before the rains started.
Despite hopes of a quick resumption, organisers of the Asian Tour and Japan Golf Tour event eventually called off play at 6 p.m with lightning still in the vicinity. Twelve players will come back on Monday morning at 7:30 a.m. to finish their round.
The event has been hit by poor weather all week and the first two days were curtailed by storms with Song and Spieth among those returning at 7:30 am on Sunday to complete their third rounds.
Song played five holes to sign for a two-under 69 while Spieth went bogey-birdie to close his third round of 70 to sit five back of the South Korean world number 204, who was looking for his first tournament win.
Large galleries came to watch the double major winner try and haul in the deficit with some final round magic but the American never really hit his customary supreme heights.
He did pick up two birdies in four holes to cut the deficit on Song but another short missed putt, which has troubled him all week, on the fifth led to a momentum-killing dropped shot.
He bounced back with birdies at eight, 11 and 15, the last one coming after a brilliant approach under some trees which chased up the green to 12 feet as he closed to within two shots of the lead.
Song stayed out in front though, calmly slotting clutch par putts on 13 and 14 to stay at 12-under before the weather interrupted.
"I am really tired, it has been a long wait. Coming back tomorrow is okay for me as the course should be in a better condition (less wet)," Song said after finishing one-under for his 15 holes.
"I will just play shot by shot and hope I can get the win. I have had a lot of second place finishes and it is time for a victory."
(Editing by John O'Brien/Sudipto Ganguly)
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