Diouf had a great chance to ease the home side's nerves when Taylor took advantage of a Dean Whitehead slip and picked him out at the back post, but this time he headed against the post.
Minutes later Chopra headed over from an Andy Reid cross as an animated Bolton boss Gary Megson looked increasingly agitated on the sidelines.
Sunderland made a triple substitution on the hour and Roy O'Donovan almost made a rapid impact when he headed a Reid centre into the path of Jones only for the striker to miss the ball completely in front of goal.
At the other end Diouf headed wide from a long row by Jlloyd Samuel.
However, the Trotters were spared an agonising last five minutes when substitute Murphy, who scored the goal that secured Sunderland's safety, headed a Taylor corner past Gordon and Reid was unable to clear off the line.
Barring a hammering at Chelsea and other results going against them, Megson's men will be in the top flight again next season.
Bolton manager Gary Megson
"I can't ask any more of them in terms of every game they have played and the effort they have put in.
"We can play better because results haven't been enough to get us into a position where we hope a club like this could be, but in terms of where we were to where we are I can't complain at all.
"We haven't played brilliantly this afternoon but we play with our hearts on our sleeve and give everything we've got."
Sunderland manager Roy Keane
"You know what you are going to get against Bolton and you have to deal with it, we are a passing team but we didn't do that.
"You're always playing for your future and we reminded the players of that.
"In the bigger picture we've managed to stay in the Premier League but we need improvement next season."
Bolton: Al Habsi, Steinsson, Andrew O'Brien, Cahill, Samuel, McCann, Nolan, Guthrie, Diouf, Davies, Taylor. Subs Not Used: Walker, Meite, Giannakopoulos, Cohen, Rasiak.
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