Sean Scannell broke the deadlock just after the half-hour mark with his first goal of the season, a long-range effort which moved in the air and left keeper Chris Weale, who should have done better, red faced.
Foxes skipper Matt Oakley came to the home side's rescue with a well-taken volley in the 58th minute but a point is not enough for a City side who are playing the chasing game for a top-six spot in the Championship.
Yakubu fired a great chance over from two yards in the second half, but ultimately Leicester lacked the invention and final ball necessary to unlock a stubborn Palace side who played 4-5-1 and countered effectively, with the visitors seeing Wilfried Zaha sent off late in injury time.
Despite the result, the two sides' respective ambitions will be shaped over their next two games, with Leicester going to play-off challengers Reading and Nottingham Forest while the Eagles face relegation rivals Scunthorpe and Doncaster.
Palace boss Dougie Freedman named a surprise starting XI with leading scorer James Vaughan, the influential Darren Ambrose, forward Steffen Iversen and midfielder Kemy Agustien relegated to the bench.
In contrast, Sven-Goran Eriksson named the same line-up who brushed aside Burnley in convincing fashion on Saturday.
But there was very little of that form on show this time around as a cagey opening half-hour passed by without a real chance of note at either end, although there was plenty of endeavour on show with both sides in desperate need of points for very different reasons.
A distinct lack of quality in the final third was evidently clear from both sides, with City's on-loan Fulham striker Diomansy Kamara scuffing the best opening disappointingly wide.
And it was no real surprise to see the game's breakthrough come from 30 yards.
Pacy Palace wide man Scannell ran unchallenged before letting fly with an effort from distance which clearly moved in the air but managed to beat Weale in the middle of his goal.
The Foxes stopper did better to deny Scannell a quick second shortly after before Paul Gallagher sent a free-kick comfortably into the hands of Julian Speroni at the other end.
The closing 10 minutes of the first half were similar to the opening 30, with very little for the 22,303 present to get excited about.
Eriksson introduced Darius Vassell at the interval in place of Gallagher.
The change did little to reverse Leicester's attacking struggles and it took a touch of class from Oakley in the 58th minute to level matters.
A ball into the box was half cleared to the edge of the area and the Foxes skipper latched onto it with a sweet volley which left Speroni with no chance.
Yakubu then missed a gilt-edged chance to put Leicester ahead, firing Vassell's low ball over the bar with the goal at his mercy, although the short pass did come to him at pace.
Patrick Van Aanholt forced a smart stop from Speroni as the Foxes pushed for a winner.
Eriksson threw on Lloyd Dyer and Steve Howard with 13 minutes remaining but Palace, with only one away win to their name all season, held firm despite the late loss of Zaha for an apparent touchline stamp on Van Aanholt.