The result sees Ukraine knocked-out of the competition, but they will exit lamenting the failure of the officials to award them a goal despite the ball clearly crossing the line from Marko Devic's effort.
For England, the result, in combination with France's surprise defeat to Sweden, is enough to see them top Group D. A huge boost given that it means Roy Hodgson's side avoid Spain in the quarter-finals and will instead take on Italy on Sunday. But it could have been very different as England had to survive long periods pegged back, particularly in the opening half.
Despite the absence of Andriy Shevchenko from the starting lineup, Ukraine began the match in inspired fashion following a stirring rendition of the national anthem at the Donbass Arena.
As has been a problem throughout the tournament, England's midfield was often caught too deep behind the ball. While it largely provided for an effective blockade on the edge of the box, as occurred with Samir Nasri's goal against them for France, that too often allowed shooting space form outside the area.
Yevhen Konoplyanka twice had decent efforts as he cut inside onto his right foot. From the other side, right-back Oleg Gusev came even closer as his stirring left-footed drive had Hart at full stretch and relieved to see the ball fractionally clear the cross bar.
It was more than half way through the first period before England finally enjoyed a concerted spell of possession and it almost paid dividends with an opening goal, very much against the run of play. John Terry pinged a fine diagonal ball out to Ashley Young and the winger cut back onto his right food for a trademark in-swinging cross that found Rooney unmarked at the far post, but, with the goal at his mercy, he put it comfortably wide.
The pressure continued from Ukraine to end the first period as gaps started to appear in England's back line. After some neat exchanges, Artem Milevskiy slipped in Yarmolennko to his right and the Dynamo Kiev star put the ball onto his favored left foot, but was just unable to get enough power or angle on his curling effort and the save was comfortable for Hart.
Yarmolenko was a constant threat and he almost single-handedly broke through the England rear guard as he waltzed past both Scott Parker and Ashley Cole in the box before Joleon Lescott finally got a challenge in to prevent a clear strike at goal.
To the anguish of the home supporters, for all Ukraine's positive work in the opening 45 minutes, it was England who snatched a vital breakthrough just three minutes after the break.
After a corner was played back out to Gerrard, the captain did well to create an opening down the right before putting in a dangerous near post cross that was twice deflected before keeper Andriy Pyatov merely helped it onto the head of Rooney, who this time couldn't miss from barely a yard out.
Clearly a bitter blow, Ukraine showed little sign at that stage of fading into the Donetsk night and could have been back on level terms but for Milevskiy heading over at the near post.
It is the co-hosts next opening that will long be talked about in Ukraine, however.
England's defenders were badly exposed as Milevskiy played in Marko Devic, who faked past Terry to put him clean through on Hart. The England stopper got half a block on the striker's shot, but the ball was looping toward the net before Terry got back to hook it out from under the cross bar.
Ukraine's players, not to mention coach Oleg Blokhin, protested vigorously that the ball had crossed the line and replays showed that they were right to do so. Although English supporters may also point to the fact that Devic was initially offside.
After the drama subsided, England began to look more composed on the ball and could have even added to their advantage.
From a James Milner cross, Pyatov again failed to cover himself with glory on a cross, palming the ball off the head of Rooney but only as far as Ashley Cole, whose effort the under fire goalkeeper just recovered to block at his near post.
With 20 minutes to go the Ukraine fans were off their feet for a final hurrah as legendary front man Shevchenko was brought on to try and save the day.
But for all their neat build-up, Ukraine struggled for a cutting edge. The closest they came to a goal late on was from another fierce long-range effort from Konoplyanka that wrong-footed Hart, who in the end made a miraculous one-handed save.
As time ran out so did any hope of a dramatic comeback as England largely comfortably saw out the final minutes. For the third-consecutive game, it wasn't the most convincing performance by England, but they deserve significant credit for progressing as group winners.