Brighton, meanwhile, remain next to bottom and will need to find more of a cutting edge if they are to avoid a quick return to the second division.
The Seagulls only shot on target came on the hour when Ian Walker diverted a free-kick from Graham Barrett over the bar at full stretch.
Defensively Brighton looked solid enough and they needed to have their wits about them, particularly in a one-sided first half.
Paul Dickov hit the post in the 21st minute and when the rebound fell to Deane he was denied by Danny Cullip's goal-line clearance. Deane missed the target with two other headers while Muzzy Izzet and James Scowcroft also went close.
In contrast Bobby Zamora, a player Adams would like to sign if Leicester return to the Premiership, got little change out of the commanding Matt Elliott.
Ironically Brighton were enjoying their best spell of the game when Leicester broke through in the 72nd minute.
Alan Rogers floated in a free-kick and Deane rose in the six-yard box to divert his header inside the left-hand post for this eighth goal of the season.