Italy caused a huge stir in Sunday's clash against England after refusing to commit any players after a tackle had been made, thus preventing any rucks from forming and allowing the visitors to legitimately stray offside.
Current England boss Eddie Jones, whose side trailed 10-5 at half-time as they struggled to respond to Italy's game plan before rallying to win 36-15, was left seething at the ruse and has called on World Rugby to revise the laws.
Jones is not the only one to have spoken out against ploy, with England fly-half George Ford suggesting it has the potential to "kill the game", but Woodward has a different view.
Writing in his column in the Daily Mail, England's 2003 World Cup-winning coach said: "I totally support Italy and their use of their innovative and inspired tactics at Twickenham on Sunday.
"It was one of those rare moments in Test rugby that, as a former coach and player, make you sit bolt upright in your seat and think, 'Wow, this is different, this is new'. What on earth do England do next?"'
Conor O'Shea's Italy went into the match lying bottom of the Six Nations table after successive defeats and with their place in the tournament under scrutiny with yet another Wooden Spoon beckoning.
England, meanwhile, were overwhelming favourites to claim a routine victory over the Azzurri that would have edged them closer to claiming back-to-back Grand Slams as well as extending their national-record winning run to 17 successive Tests.
Woodward added: "Italy are scrapping for respect and pride, both personal and national after many have criticised their right to an automatic place in the Six Nations.
"What we did see at Twickenham was a very gutsy and clever, if ultimately unsuccessful, response from a wounded Italy side that felt under pressure.
"Against a superior team and a rugby nation with infinitely more resources, Italy went down fighting and scheming and plotting. It was behind the lines - literally - guerrilla war and I found it compulsive viewing. It's what David always has to do if he is to stand any chance against Goliath.
"The tactic is entirely legitimate and it was fascinating to watch it unfold in a big-match situation."