Having lost nine of their first 10 league matches Palace were among the favourites to be relegated, but the arrival of Tony Pulis has improved their fortunes and Bolasie was quick to praise the impact of his manager.
"The manager has come in and done a brilliant job. I can't thank him enough, and he's proved plenty of people wrong, BBC Sport quotes him as saying.
"We've got 40 points now and we feel safe enough."
Palace have now won their last four matches in the Premier League.