England raced to a 40-5 victory, but the size of their success could not mask an often error-strewn display.
Woodward's men posted five tries during a blistering opening 21 minutes - but then went almost 50 minutes without scoring another point.
Italy dominated much of the game in terms of possession, and England were never able to turn a 33-0 advantage into the points landslide a Twickenham full house expected.
Full-back Josh Lewsey, deputising for the injured Jason Robinson, took his chance superbly and scored two tries - while there were also touchdowns for Mike Tindall, Dan Luger, James Simpson-Daniel and Steve Thompson.
Captain Jonny Wilkinson booted four conversions before going off injured early in the second half, while scrum-half Matt Dawson also landed a conversion.
Despite the stop-start effort, England will clinch a clean sweep if they win their remaining fixtures against Scotland and unbeaten Ireland in Dublin.
"It was a wonderful first 20 minutes, and I am very pleased with that," said Woodward.
"I thought that Josh Lewsey and Mike Tindall were outstanding, while Ollie Smith and Mike Worsley did well after going on for their first caps.
"After the first 20 minutes, though, we couldn't get the ball off the Italians. It is a strange game to analyse, and the dressing room was very quiet afterwards.
"But it is hats off to Italy. From 33-0 down, to dominate the rest of the game like they did was pretty impressive."