Danns, who left Selhurst Park on a free transfer in the summer, was recalled to the starting line-up with the Foxes without a victory in their last five outings.
And the midfielder opened the scoring with his third goal of the season before setting up Sol Bamba for the second.
Palace pulled one back through Jonathan Parr but could not find an equaliser as Leicester held on, despite a late red card for Steve Howard, to register only their third away win of the season and inflict Palace's second home defeat.
As well as bringing in Danns, City manager Nigel Pearson reacted to their recent slump by handing a full debut to 18-year-old Liam Moore, a first run-out in 16 months for Tom Kennedy and a return for Aleksandar Tunchev, whose last appearance was for Palace on loan in October.
Palace were also much changed due to a sickness bug which claimed captain Paddy McCarthy an hour before kick-off as well as regular goalkeeper Julian Speroni.
And it was Speroni's replacement, Lewis Price, who was at fault for the opening goal after 19 minutes.
Price thumped what should have been a routine clearance into the back of one of his own defenders and the ball fell to Danns, who was able to curl his shot back past the red-faced keeper and into the net.
The goal stunned Palace, who had been the better side in the early stages and almost opened the scoring when Owen Garvan fired narrowly wide.
They attempted to hit straight back and Wilfried Zaha drove over the crossbar, but instead they found themselves two down after 36 minutes with Danns the architect again.
The former Colchester and Birmingham midfielder swung in a free-kick which was helped on by David Nugent and nodded in at the far post by centre-half Bamba.
But Palace did manage to pull one back before half-time when Norwegian full-back Parr's curling effort deceived Foxes keeper Kasper Schmeichel and flew into the back of the net.
And they almost went in level at the interval after Garvan played in Glenn Murray but Schmeichel spread himself well to keep out the striker's effort.
Murray went close again at the start of the second half, running on to a clever angled pass from Nathaniel Clyne but pulling his shot across goal and just wide of the far post.
Schmeichel also denied Zaha and Jermaine Easter and Chris Martin's shot was deflected wide before Leicester substitute Howard said something which the assistant referee did not take kindly to and was shown a straight red card.
But the 10 men saw out the final few minutes to propel big-spending City back towards the play-off places.