A win by the former US Masters champion would give him the first treble in European golf since Australian Peter Thomson captured the Open Championship from 1954 to 1956.
'I have got to fancy my chances now even though there are some good players not far behind,' Woosnam said.
Even though he twice lost a golf ball - hitting his drive into the bushes at the third and his seven- iron tee shot into more shrubbery behind the 14th - Woosnam took a one-stroke lead over Argentinian Eduardo Romero.
Ireland's Darren Clarke, who had a five-shot half-way lead, slipped down to third place after taking 73 for 199, with fellow Irishmen Paul McGinley (69) and Eoghan O'Connell (64) sharing fourth place with former champion Mark McNulty.
Woosnam birdied the last two holes to stamp his authority on proceedings after Clarke had seen his big lead cut to just one shot at the turn when he hooked his six- iron second shot out of bounds at the ninth.
The 23-year-old Ulsterman made further mistakes to lose shots at the 11th and 15th and Woosnam seized his chance.
'I have done what I set out to do when I came here, and that is get my game in shape for the Open Championship,' Woosnam added. 'Now win or lose I am looking forward to the challenge.'
The Welshman two-putted the long 17th for his fifth birdie, then ran down a 15-foot putt on the last green to overhaul Romero, who had set the clubhouse target by hitting a 65, which included six birdies.
Romero might have been alongside Woosnam had he not topped his drive only 50 yards at the 17th. Earlier he had missed a putt of 20 inches at the sixth.
Woosnam, is now 43 under par for the last 11 rounds he has played on the course, 2,500 feet above Monte Carlo.
Zimbabwe's McNulty, whose record in Monte Carlo is also superb, comes into that category after chipping in from 15 yards for an eagle-three at the first and also claiming four birdies in a round of 66 to total 200.
He has never been over par on the Mont Agel course, his 19 rounds producing a grand total of 56 under the card.
MONTE CARLO OPEN (Mont Agel) Leading third-round scores (GB or Irl unless stated): 197 I Woosnam 66 65 66. 198 E Romero (Arg) 67 66 65. 199 D Clark 66 60 73 199. 200 P McGinley 65 66 69; M McNulty (Zim) 67 67 66; E O'Connell 70 66 64. 202 M A Jimenez (Sp) 67 68 67; R Davis (Aus) 68 66 68; C Rocca (It) 64 71 67. 203 K Waters 66 70 67; D Smyth 72 67 64; J Van de Velde (Fr) 71 67 65; P Walton 68 66 69; J Ristrom (Swe) 70 64 69; P U Johansson (Swe) 68 65 70; P Mitchell 68 65 70; J Sewell 67 68 68. 204 R Gonzalez (Arg) 71 62 71; T Levet (Fr) 69 70 65; S Tinning (Den) 74 64 66; T Johnstone (Zim) 71 66 67. 205 R Boxall 74 62 69; A Forsbrand (Swe) 73 67 65; H Baiocchi (SA) 73 65 67; M Sunesson (Swe) 73 65 67. 206: P Senior (Aus) 67 66 73; G J Brand 67 71 68; S Ballesteros 70 69 67; M Gates 74 63 69.Reuse content