'They have to catch me. I'm not going to back off,' Singh said.
He has put together the best opening three rounds ever at the TPC at The Woodlands, shooting a 6-under-par 66 Saturday for a three-stroke lead over Darren Clarke.
At 18-under 198, Singh matched the tournament record for relation to par set by Curtis Strange in his 1980 victory at the par-71 Woodlands Country Club.
'It's Vijay's tournament to lose,' Jose Maria Olazabal said after a 64 left him in third place, five shots back. 'If he keeps on playing the way he's doing at the moment, I don't think we have much of a chance to beat him.'
Singh, looking for his first PGA Tour victory since the 2000 Masters, was nearly flawless for a third consecutive day.
Northern Ireland's Clarke, who trailed Singh by two shots going into Saturday, had a 67, but lost ground to the leader.
'Vijay kept flagging it,' he said. 'I'm quite pleased to have a chance. I think with the way Vijay's playing, if he keeps playing like that, he's going to be very, very difficult to catch.'
Olazabal of Spain was next at 203. He had nine birdies in his 64, his best round of the year and the lowest round of the tournament.
Other international players in contention included Japan's Shigeki Maruyama at 11-under after a 66. That was one shot better than South Africa's Rory Sabbatini, who also had a 66, and Australia's Greg Norman, whose second consecutive 68 left him eight shots off the lead.
Brandt Jobe, who lives near Dallas, had a 69 and was tied with Maruyama. His 205 made him the lowest-scoring American-born player.
Singh parred the first three holes, then started a birdie barrage, collecting six over the next eight holes. His two-putt for birdie at the island green 13th hole put him at 19-under and six shots ahead.
But at the par-3 No. 14, he went 20 yards past the pin and over a bunker and he settled for a bogey -- his first since a bogey at the same hole in the opening round Thursday. Those are his only bogeys of the tournament. He finished the round with four consecutive pars.
'I thought I left a few out there but I guess we all do,' Singh said. 'I was very aggressive... I just have to focus on what I'm doing and not what the rest of the guys are doing and take the opportunities that I can. My game plan (Sunday) will be just think about what I'm doing and nobody else. Everything will be OK, I think.'
Clarke started with five consecutive pars and was trailing his playing partner by six shots when Singh ran into trouble at the 14th.
'I just had to keep on doing what I was doing,' Clarke said. 'I was still giving myself opportunities at the same time he was hitting it in close.
'I just hung in there and made a couple of birdies toward the end to close the gap.'
Full-field scores from the Shell Houston Open