Despite a far from impressive performance, Dott will join fellow Scots Stephen Maguire and John Higgins in round two at York's Barbican Centre.
The former world champion admitted opponent Martin Gould was the better player, but at 5-3 down he rallied to capitalise on the missed chances of his opponent and win the deciding match 6-5..
Shaun Murphy, the 2008 champion, awaits Dott in the second round after beating Robert Milkins 6-3, and the Larkhall potter is aware he must do better.
"I couldn't have cared less who won out of Shaun and Robert," said 35-year-old Dott. "I just hoped it had gone to 6-5 to be honest.
"I didn't play great and Martin was the better player but I have won games like that in the past.
"Not every player can play pretty badly and feel awful when you are playing but still manage to win the game.
"My 'B' game is obviously working, I just need to bring my 'A' game because if Shaun brings any sort of 'A' game then that will be too much for me."
Of the three Scots, the Glasgow-born Maguire was the most impressive after making three successive century breaks to beat Ireland's Fergal O'Brien 6-3. This result only improves when it is noted that he previously trailed 2-1.
"Something clicked in the end and the balls started splitting nice, it went my way and I got my break," he said.
"I'm not going to keep that form up, but if I keep half of that up it is going to take someone to play well to beat me."
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