It was a dismal performance from the Lions outfit they were comprehensively out-played for long spells and never fully recovered from a nervy opening which saw them concede an early try to Jose Nunez Piossek.
There was some encouragement to be taken from an impressive performance by Jonny Wilkinson playing his first international since the World Cup final in November 2003 with the England fly-half booting 20 points.
He landed the penalty which secured a share of the spoils, set up the Lions' only try scored by Ollie Smith in the 17th minute and gave further evidence that he is on the path to recovering his best form.
But the star of the night was Argentina fly-half Federico Todeschini who landed 20 points in a flawless kicking display that laid the foundations for their challenge.
The Pumas put on the pressure helped by a knock-on from Ireland hooker Shane Byrne and were rewarded with a penalty which fly-half Federico Todeschini sent between the uprights.
The Millennium Stadium crowd was then stunned into silence as Argentina added to their score with a beautifully-worked try created by skipper Felipe Contepomi in the seventh minute.
Full-back Geordan Murphy took a tricky up-and-under but the ball was turned over at the breakdown and swiftly fed to Contepomi who sliced through the Lions' midfield before supplying the scoring pass to Piossek.
Todeschini added the conversion and then a penalty to give the Pumas a 13-0 lead they richly deserved given their early superiority, with Woodward's men paying a high price for their nervous start.
But the Lions burst into life in the 17th minute when a line-out catch and drive made valuable yards before the ball was released to Wilkinson who drew Todeschini and fed Ollie Smith with the Leicester ace racing home. Wilkinson converted.
Todeschini punished the Lions' poor discipline with his third penalty.
Two Wilkinson penalties sandwiched three points from Todeschini as the Lions made a promising finish to the first half, and it would have been better had Williams not overlooked a two-man overlap.
They had to settle for a third Wilkinson penalty on the stroke of half-time, but it would have been a different story had Danny Grewcock shown better handling skills as the Lions created another clear overlap.
It was then Wilkinson's turn to make an impressive break and when the Pumas strayed offside in the next phase, the England skipper was on hand to level the score with a simple penalty.
Todeschini replied in kind to restore Argentina's slim lead and he then extended it with his sixth penalty after the Lions had been penalised for pulling down a rolling maul which had made 30 yards.
Wilkinson began to stamp his authority on proceedings, making a fine break and setting up another for Murphy with a bullet pass, before being victim to a high tackle which allowed him to land another penalty.
By now Woodward had used all but Ronan O'Gara and Lawrence Dallaglio from the replacements bench but the new arrivals had added little to the Lions' game in the face of Argentina's continued resistance.
Expectations that the Pumas would run out of steam going into the last 10 minutes proved ill-founded and they defended heroically as the Lions put them under the cosh in the dying moments.
The cream of British and Irish rugby still had time in which to snatch victory and they went desperately close only for Gordon D'Arcy to drop a pass with the line begging. Instead, they had to settle for a draw as the Pumas conceded a penalty eight minutes into injury time which Wilkinson sent between the uprights.
LIONS: Murphy, Hickie, Smith, D'Arcy, S Williams, Wilkinson, Cooper, Owen, Moody, Corry, Grewcock, O'Callaghan, Hayes, Byrne, Rowntree.
ARGENTINA: Stortoni, Nunez Piossek, Arbizu, F Contepomi, Leonelli, Todeschini, N Fernandez Miranda, Manuel Leguizamon, Schusterman, Genoud, Sambucetti, Bouza, Reggiardo, Ledesma, Mendez.
Referee: S Dickinson (Australia)