But when substitute Tomasz Radzinski pulled a goal back in the 76th minute, Sunderland were forced to defend in numbers to protect their lead and give themselves a chance of overhauling the lowest number of top-flight points accumulated by Stoke City in 1985.
Caretaker manager Kevin Ball made four changes to the side comprehensively beaten by Arsenal on Monday, including the surprise inclusion of Andy Welsh.
The left winger returned from a loan spell at Leicester City and was thrown in the action along with Steve Caldwell, Le Tallec and Justin Hoyte.
Luis Boa Morte was close to giving Fulham a sensational first minute lead, whipping over a right-wing free-kick that almost deceived goalkeeper Kelvin Davis on its way across the face of goal.
Steed Malbranque hit a volley inches too high as the visitors kept up the pressure, but Mark Crossley needed two attempts to keep out Dean Whitehead's crisp 25-yard drive after Welsh had linked up cleverly with George McCartney down the left.
Fulham suffered a blow when skipper Boa Morte limped off in the 18th minute to be replaced by Radzinski, but five minutes later were not to far off taking the lead as Liam Rosenior almost scored from the halfway line with a quickly taken free-kick.
Sunderland, however, made the breakthrough in the 32nd minute. Welsh again linked up well with McCartney and from his low centre Le Tallec nipped in ahead of Ian Pearce to beat Crossley with a deft header.
Fulham responded immediately with Gary Breen coming to the rescue with a last-ditch tackle to prevent Heidar Helguson from latching on to Malbranque's through ball and then Radzinski was just off target with Davis at full stretch.
But Sunderland, who had Caldwell and McCartney booked for fouls, went in at half-time in the lead in their search for that elusive first home win.
And they missed a great chanced to go further ahead five minutes into the second period. Nyron Nosworthy galloped 50 yards down the right before crossing to Hoyte who completely mis-kicked in front of goal.
In the heat of the battle Fulham had Simon Elliott, Philippe Christanval and Pearce booked then fell further behind in the 57th minute.
Nosworthy, pushing forward at every opportunity, forced Crossley into a diving save but the keeper failed to hold on and Brown gleefully swept home the loose ball from six yards.
The game changed completely in the 76th minute when Radzinski cut in from the right to unleash a thundering left-foot shot that left Davis helpless.
Two minutes later substitute Collins John missed a great chance to equalise but after shrugging off Breen, he fired into the side-netting to the dismay of the handful of visiting supporters behind the goal.
Sunderland, however, were not to be denied their long overdue victory and at least salvaged some pride from a disastrous campaign.