After Carrick was surprisingly withdrawn for Frank Lampard, Rooney was booked as the pressure began to build. However, captain Gerrard ran through in the closing stages to prod past Szczesny and seal a hard-earned triumph.
"We knew it was going to be a tough game," Rooney told ITV. "But we played some great stuff and getting the goal in the first half gave us the belief and confidence that we could go on to win the game. Thankfully, Stevie's got the second goal to see us qualify.
"We've always remained positive no matter what has been said. We've shown we're a good team and we're looking forward to a few friendlies before the tournament but we're excited."
Elsewhere, Nani captained Portugal in Cristiano Ronaldo's absence and celebrated with a stunning first-half strike with his left foot following a fine move. Portugal ran out 3-0 victors against 10-man Luxembourg but have to settle for a play-off place with Russia winning Group F.
Patrice Evra's France are also in the play-offs despite a 3-0 home beating of Finland. The left-back was cautioned on the hour mark as Spain top Group I following their 2-0 success against Georgia.
ENGLAND v Poland - Michael Carrick, Phil Jones, Wayne Rooney, Chris Smalling, Danny Welbeck
FRANCE v Finland - Patrice Evra
Turkey v NETHERLANDS - Robin van Persie
PORTUGAL v Luxembourg - Nani