Overseas signing Usman Khawaja blasted a debut century for Glamorgan to leave Warwickshire needing 294 runs to wins at Edgbaston.
Khawaja struck 125 from just 143 balls and was ably supported by Captain Chris Cooke who hit 59 as the pair put on 115 for the 5th wicket.
"I was still a bit jet-lagged in the first innings and didn't feel right, but it was nice to get some time in the middle," said Khawaja.
"I came out with a bit more positive intent. I felt good from the start.
"We knew a lead of 250-plus would be very nice when I came in. We got close to 300 and it can be one of those wickets where it can be a bit of a grind. It's not a very fast wicket. Hopefully we'll keep grinding, keep restricting them, bowl 10 good balls and win the game.
"The bowlers here bowl differently in different conditions, but I love coming to England and playing county cricket because it it so different from Australia. It's a nice challenge."