Geordan Murphy set up Leon Lloyd for the first try before Leeds went ahead through Andre Snyman's converted try.
Matt Cornwell's touchdown on half-time put the Tigers ahead but Chris Murphy's try while Tigers captain Deacon was in the sin-bin restored the Tykes' lead.
Broadfoot's boot kept Leicester in the game before Deacon's vital late score.
Leeds boss Phil Davies: "We got good field position but just didn't capitalise on it," Davies said.
"The players put in a phenomenal effort but again came up short after some elementary errors. It's pretty disappointing really."
Leeds: Balshaw, Rees, Jones, Snyman, Biggs, De Marigny, Marshall, Shelley, Bulloch, Kerr, Murphy, Palmer, Dunbar, Parks, Crane.
Replacements: Gerber for Shelley (40), Rawlinson for Bulloch (76), Hooper for Murphy (62), Thomas for Crane (62). Not Used: Care, Stimpson, Ross.
Leicester: Murphy, A. Tuilagi, Smith, Cornwell, Lloyd, Broadfoot, Healey, Rowntree, Taukafa, Holford, L. Deacon, Hamilton, B. Deacon, Skinner, Johnson.
Replacements: Varndell for Lloyd (68), Chuter for Taukafa (51), Jennings for Johnson (51). Not Used: Young, Cullen, Ellis, Hipkiss.
Att: 7,143
Referee: Rob Debney (Leicestershire)