England narrowly beat Ukraine 1-0 thanks to a Wayne Rooney header to win their Euro 2012 group and set up a quarter-final tie with Italy.
The returning Rooney, having missed a gilt-edged chance in the first-half, nodded in an easy goal early in the second-half from Steven Gerrard's cross for his first international strike in nine months.
Yet karma smiled on the Three Lions when Marko Devic's effort looped over the goal-line as the scurrying John Terry cleared. Neither linesman nor the official beside the goal acknowledged a clear goal.
England started sluggishly as Ukraine - who had to win - exerted pressure with some slick passing yet rarely tested Joe Hart. Andriy Yarmolenko drew the most noteworthy save from the Manchester City stopper after engineering space up against Ashley Cole.
Although Hodgson's side again failed to look comfortable in possession, they forged the best chance of the half. Ashley Young's inswinger found Rooney at the far post, but he mistimed his header and glanced wide.
However the 26-year-old made amends in the 48th minute. Gerrard - the man of the match - saw his cross deflect its way to the far post after Andriy Pyatov failed to hold on, where his fellow Scouser was waiting on the goal line to head in.
But again England retreated rather than attempt to build on their lead. Artem Milevskiy missed a golden opportunity from a corner before Devic - who was a yard offside when he received the ball - beat Joleon Lescott to fire goalwards for the game's talking point.
Hart's touch elevated the ball but did not stop its intended destination, as Terry raced back dutifully and cleared from underneath the crossbar, but the ball had comfortably passed the goal-line. Oleg Blokhin, the Ukrainian coach, was seething when it became apparent an equaliser had not been awarded.
Andriy Shevchenko arrived in a bid to galvanise the joint hosts, but they, like Poland, were eliminated as England recorded their first clean sheet at the Euros.
News had already filtered through that Seb Larsson had doubled Sweden's lead over France in the other group match after Zlatan Ibrahimovic's stunning opener, and Hodgson's charges were all but confirmed as group winners.
They will face Group C runners-up Italy on Sunday while France play Spain in a repeat of the Euro 2000 quarter-final. The Three Lions have not played the Azzurri in a competitive match since the Glenn Hoddle era, in 1997.