The Collaborative International Dictionary of English v.0.48:

Finesse \Fi`nesse"\ (? or ?), n. [F., fr. fin fine. See Fine,
   a.]
   1. Subtilty of contrivance to gain a point; artifice;
      stratagem.
      [1913 Webster]

            This is the artificialest piece of finesse to
            persuade men into slavery.            --Milton.
      [1913 Webster]

   2. (Whist Playing) The act of finessing. See Finesse, v.
      i., 2.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Finesse \Fi*nesse"\, v. i. [imp. & p. p. Finessed; p. pr. &
   vb. n. Finessing.]
   1. To use artifice or stratagem. --Goldsmith.
      [1913 Webster]

   2. (Whist Playing) To attempt, when second or third player,
      to make a lower card answer the purpose of a higher, when
      an intermediate card is out, risking the chance of its
      being held by the opponent yet to play.
      [1913 Webster]

WordNet (r) 3.0 (2006):

finesse
    n 1: subtly skillful handling of a situation [syn: delicacy,
         diplomacy, discreetness, finesse]

Moby Thesaurus II by Grady Ward, 1.0:

229 Moby Thesaurus words for "finesse":
   Italian hand, ability, acquired taste, acuteness, address,
   adeptness, adroitness, airmanship, angle, appreciation,
   appreciation of differences, appreciation of excellence,
   appreciativeness, art, artfulness, artifice, artisanship,
   artistic judgment, artistry, astuteness, beguile, bluff, bravura,
   brew, brilliance, cabal, cageyness, callidity, canniness,
   capability, capacity, choiceness, civilized taste, civilizedness,
   cleverness, collude, collusion, command, competence, complicity,
   complot, con, concoct, confederacy, connivance, connive,
   connoisseurship, conspiracy, conspire, contrivance, contriving,
   control, cook up, coordination, countermine, counterplot, covin,
   craft, craftiness, craftsmanship, critical niceness, criticalness,
   cultivated taste, cultivation, culture, cunning, cunningness,
   daintiness, dash, deceit, deceive, deception, deep-laid plot,
   deftness, delicacy, delude, device, dexterity, dexterousness,
   dextrousness, diplomacy, discretion, discriminating taste,
   discriminatingness, discrimination, discriminativeness, dodge,
   efficiency, elan, elegance, engineer, engineering, excellence,
   expedient, expertise, expertness, exploit, facility,
   fastidiousness, feel, feeling, finagle, finagling,
   fine Italian hand, fine palate, fool, foxiness, frame, frame up,
   frame-up, game, gamesmanship, good taste, grace, gracefulness,
   gracility, graciosity, graciousness, grip, guile, handiness, hatch,
   hatch a plot, hatch up, hoodwink, horsemanship, ingeniousness,
   ingenuity, insidiousness, intrigue, inventiveness, jockey,
   judiciousness, knack, know-how, lay a plot, little game, machinate,
   machination, making distinctions, maneuver, maneuvering,
   manipulate, manipulation, marksmanship, mastership, mastery,
   niceness, niceness of distinction, nicety, one-upmanship, operate,
   outwit, palate, panache, play, plot, plotting, polish,
   practical ability, proficiency, prowess, quality, quickness,
   readiness, refined discrimination, refined palate, refinement,
   resource, resourcefulness, rig, rigging, ruse, satanic cunning,
   savoir-faire, savvy, scheme, schemery, scheming, seamanship,
   selectiveness, sense, sensibility, sensitivity, sharpness, shift,
   shiftiness, shrewdness, skill, skillfulness, slipperiness, slyness,
   sneakiness, sophistication, sophistry, stealth, stealthiness,
   stratagem, strategy, style, subtilty, subtleness, subtlety,
   suppleness, tact, tactfulness, talent, taste, tastefulness,
   technical brilliance, technical mastery, technical skill,
   technique, timing, trick, trickiness, twist and turn, underplot,
   virtuosity, wangle, wariness, web of intrigue, wile, wiles,
   wiliness, wire-pulling, wit, wizardry, workmanship