Roy Hodgson's men knew that only a victory would guarantee their ticket to Brazil and their attacking approach was rewarded in the 41st minute when Wayne Rooney guided a header past Wojciech Szczesny from Leighton Baines' left-wing cross.
Poland played their part in an open and exciting game and England had to withstand some anxious moments, but they carved out several of their own chances and a fabulous solo goal from captain Steven Gerrard after 88 minutes finally put the result beyond doubt and secured top spot in Group H ahead of Ukraine.
England made two changes from the side that beat Montenegro on Friday to put a place in Brazil within reach, as Michael Carrick came in for Frank Lampard and the suspended Kyle Walker was replaced by Chris Smalling.
But the new-look defence lacked cohesion in the early stages as Robert Lewandowski was afforded space to gallop into as Poland broke from deep inside their own half. One of Europe's most feared strikers had virtually reached the edge of the box before anyone closed in, too late to stop Lewandowski firing at goal, although Joe Hart saved easily.
The next scare came when Adrian Mierzejewski was not picked up by Andros Townsend as he broke over halfway and, when Jakub Blaszczykowski allowed the square pass to run through his legs, Lewandowski arrived, unopposed, to carry it on.
It was to Hodgson's relief the Borussia Dortmund man had been exhausted by his long surge. First he stumbled, then he dragged his shot wide, when virtually the entire stadium expected the ball to be nestling in the net.
England gradually started to dominate but Poland goalkeeper Szczesny revived memories of Jan Tomaszewski in 1973 as he saved from Townsend, Danny Welbeck twice and Rooney.
In addition, Smalling came agonisingly close to touching home Gerrard's free-kick, Sturridge nearly profited from some kamikaze defending in the Polish box and the lively Townsend curled a shot against the bar that had Carrick raising his arms in celebration.
With Welbeck also lashing wide after tip-toeing over a pile of prone bodies, it began to feel like one of those evenings.
But, as half-time approached, Rooney struck. The goal was typically English in its simplicity but due credit should be paid to Carrick, for having the vision to pick out Baines with a first-time pass, and the Everton man for the brilliance of his delivery.
Had Gary Cahill nodded Gerrard's corner in at the start of the second half, or Grzegorz Krychowiak toed the ball home when his sliding intervention left Szczesny stranded and helpless, England could have started to breathe.
Instead they were indebted to Hart's bravery as he blocked Lewandowski's delicate effort after he had nipped behind England's tiring defence.
There were other scares for England as Poland looked to end their campaign with a flourish in front of an estimated 18,000 away fans, but Hodgson's men stayed positive.
Szczesny denied Rooney and Sturridge, before Gerrard, driving into the visitors' box like the leader he so obviously is, chipped over the keeper to send England into raptures.