The Fulham faithful could never had imagined seeing their side sit just behind Chelsea, Arsenal and Manchester United in the table, but two late strikes from Sean Davis and Sava maintained their unbelievable run of form.
It could have been a different story if Bolton had opened the scoring after just ten seconds of the game.
Simon Charlton's long ball into the box was cleverly flicked on Kevin Davies. The ball fell nicely to Kevin Nolan who found himself completely unmarked inside the box.
Nolan, on the half-volley, fired a low right-foot effort which produced a superb save from Edwin Van der Sar.
Nolan had anther golden chance to break the deadlock for Bolton on 33 minutes. Charlton's cross from the right fell perfectly for Nolan whose acrobatic scissor kick was only just held onto by Van der Sar in the Fulham goal.
Fulham created the best opening of the first half on 37 minutes when Steed Malbranque's throughball released Junichi Inamoto clean through on goal.
The Japanese international burst his way into the penalty box, but with just Jussi Jaaskelainen to beat, he fired his effort high over the bar.
And Fulham were made to pay when Bolton opened the scoring after 53 minutes.
Jay Jay Okocha's long throw-in was flicked on by Ivan Campo into the path of Davies, who made no mistake firing a sweet volley past the stranded Van der Sar into the corner of the net.
And the former Southampton star should have added his second of the game just two minutes later.
Ricardo Gardner's cross from the left found Davies completely unmarked just five yards from goal, but he headed the ball into the ground and saw his effort bounce over the crossbar.
Bolton came close once again to extending their lead on 66 minutes when Youri Djorkaeff released Campo into the box, but he struck his effort straight into the path of the Fuham keeper.
Fulham blew a golden chance to snatch an equaliser on 72 minutes when Moritz Volz's cross into the box fell for Malbranque, whose close-range header skimmed the post.
But they made Bolton pay for those earlier missed opportunities 60 seconds later when substitute Barry Hayles weaved his way into the box before squaring the ball across to Davis.
The former England Under-21 star fired a sweet shot past Jaaskelainen into the top left-hand corner.
And the game turned on its head on 76 minutes when Fulham added a second. Hayles once again caused all kinds of problems for the Bolton defence.
The ball fell kindly to fellow substitute Sava, whose half-volley from six yards out was smashed past the Bolton keeper to send the Fulham fans into jubilation.
Fulham just managed to hold onto the three points by the skin of their teeth in injury time when Mario Jardel's cross found Okocha, but his close-range header came back off the post.