Stanislas lashed in his fifth goal of the season and Martin Paterson's late close-range header gave Sean Dyche's side their third win at home in 10, consigning Ipswich to their first defeat in four games.
Ipswich went into the game on the back of one defeat in nine and should have taken the lead in the opening exchanges but Patrick Kisnorbo headed Anthony Wordsworth's corner over the crossbar.
This had the feel of an end of season game early on, and it took 18 minutes for Burnley to register an effort through a Sam Vokes header but it never troubled Scott Loach.
The second half started brighter, with both goalkeepers called into action early on. First Daryl Murphy's close-range header was thwarted by Lee Grant and a minute later, Paterson let fly from 20 yards but Loach saved comfortably.
Second-half substitute Stanislas took just six minutes to break the deadlock on the hour mark when he surged forward before unleashing an unstoppable strike from 20 yards into the top-left corner.
It gave Dyche's side impetus and Ipswich were indebted to Roach moments later when Kieran Trippier's cross was met by Vokes, who saw his header saved.
For the first time in the afternoon, Ipswich exerted some real pressure. Tommy Smith's shot on the edge of the area was blocked by Kevin Long, and although Smith picked up the rebound his goalbound shot was stopped by Grant.
But the Clarets continued to look dangerous. Paterson broke the offside trap with 18 minutes to go and slid the ball to Dean Marney but his outstretched leg could only divert the ball wide.
Paterson was in the action again three minutes later when Danny Ings threaded the ball through to the Northern Ireland international, who lashed over from 12 yards. And their dominance was rewarded three minutes from time and Paterson celebrated his 150th league appearance for Burnley in style. Ings swung in another dangerous corner and Paterson got the final touch.