His 2005 pride of Lions failed to shine in front of 61,569 expactant spectators in Cardiff, in only the Lions' third outing in Europe in their 117-year history.
The Pumas almost pulled off a ground-shaking win through winger Jose Maria Nunez Piossek's early try and an immaculate haul of 20 points from the right boot of fly-half Federico Todeschini.
But fit-again fly-half Jonny Wilkinson saved the Lions blushes by setting up Leicester centre Ollie Smith for the home side's only try, and matching his opposite number kick-for-kick, including a last-gasp penalty leveller, eight minutes into injury-time.
A relieved Woodward admitted afterwards: "We didn't expect to draw, we were hopeful to win the game but the biggest thing was to get through the game without any injuries.
"It was a difficult game tonight. It was the first time the Lions have played a game like this before going on tour. I am just delighted no-one is injured and we can go on and prepare for the Bay of Plenty game (June 4).
Woodward singled out his former World Cup-winning number 10 Wilkinson for special praise, saying: "Jonny did well. He, like all the other players, found it difficult with the new combinations. The way he played and kicked speaks for itself."
Wales' Michael Owen, captain-for-the-night in the absence of tour skipper Brian O'Driscoll, who watched on from the stands, said: "We were lucky to get away with the draw.
"It was bitterly disappointing, but we've got to take the positives out of the game.
"This happens in rugby. We have highs and we have lows. This isn't a low, it's a disappointment, but we have to fight back," added the number 8.