Both players scored in the 3-2 victory over bogey side Sweden to fully justify Hodgson's faith in them - and give the coach an enviable selection headache for the Three Lions' final group match against Ukraine with Wayne Rooney set to return from suspension.
Theo Walcott also comes in for widespread praise after what is seen as a match-turning performance off the bench, as England put themselves in a strong position to qualify from Group D for the quarter-finals.
As such, the general feeling emitted from Saturday's back pages is justifiably optimistic, with headlines such as 'Game on', 'Oh Danny joy' and 'England ecstasy' summing up the mood.
Here we bring you what some of the top columnists from the national papers thought about the performance.
Oliver Holt (Daily Mirror): "Roy Hodgson might as well have walked out into his technical area at the Olympic Stadium in platform shoes. Or hung a disco ball from the ceiling of the England dressing room. Or decorated it in avocado green for the night. He was accused of crimes against fashion by picking Andy Carroll in a 4-4-2 against Sweden last night. But after a see-saw night when England flirted with disaster, Hodgson proved his doubters wrong again. Not just because Carroll scored a magnificent header to open the scoring in the first half. But because when everything was going wrong and it looked as if England would be going home early, Hodgson acted fast. He didn’t stick with something that had stopped working. He updated. He modernised."
Paul Haywood (Daily Telegraph): "Andy Carroll and Danny Welbeck: 10 caps between them and two international goals before this game. Zlatan Ibrahimovic: 78 caps and 32 goals for Sweden. On paper one Swedish striker was worth two English ones until Carroll and Welbeck scored with head and heel respectively and helped Roy Hodgson’s side to a first competitive victory against their Scandinavian nemesis. A draw with Ukraine will see England through after a match that was anything but a night in a tactical museum. In fact, it turned into a hoot; shapeless desperation, with Theo Walcott’s cameo swinging the game England’s way and turfing Sweden out of the competition."
Oliver Kay (The Times): "To paraphrase a certain Swedish former England manager, first half good, second half uncategorisable. This was a night on which England combined the sublime with the ridiculous — and the sublime won out, thanks to a late goal made by Theo Walcott and executed in wonderful fashion by Danny Welbeck. At the end of it all, Roy Hodgson puffed out his cheeks in relief. It was the result that he had been looking for, but perhaps not quite the performance. He likes his teams to be measured and composed, but, for a period early in the second half, this was chaotic, with Olof Mellberg forcing an own goal from Glen Johnson and then putting Sweden 2-1 ahead, leaving England with a mountain to climb in the final half-hour."
Simon Stone (Independent): "When the dust finally settles, Hodgson will take huge satisfaction from the knowledge both his bold selection moves, picking Andy Carroll and introducing Theo Walcott, paid off handsomely. Less palatable will be replays of the atrocious defending that forced England to launch their memorable fightback after a half-time lead turned into a deficit as Olof Mellberg twice took advantage of opponents' slackness to put Sweden in front."
Steven Howard (The Sun): "It was 14 traumatic minutes that changed England’s European Championship campaign. Fourteen minutes that saw England go from defeat to victory, veering from one of Kipling’s twin imposters - disaster - to the other of triumph. Fourteen minutes that saw England score twice through Theo Walcott and Danny Welbeck and avoid defeat by Sweden and likely expulsion from the tournament. Now England require no more than a draw against co-hosts Ukraine in Donetsk on Tuesday to reach the quarter-finals — though they will need to both win and fill their boots to finish top of the group and so avoid Spain. But, incredibly, it also leaves manager Roy Hodgson with problems. Problems any manager would love to have. Which of his young lions to leave out with the return of Wayne Rooney after his two-match suspension."
Paul Joyce (Daily Express): "The curse has been lifted, the hoodoo banished and ambition has been breathed into England’s European Championship campaign. More important than the fact that his side have belatedly joined Europe’s party, playing their part in a breathless encounter here last night, Roy Hodgson was able to celebrate a victory that leaves the country’s destiny in their own hands. When Danny Welbeck turned home Theo Walcott’s centre with a delicious pirouette with time running out, the momentum of not only this contest shifted once again but the dynamics of Group D. And with Wayne Rooney to come back with his suspension over, England will be hopeful of claiming the result they require, though in slightly less frenetic fashion."
Martin Samuel (Daily Mail): "At England's centre of progressive thinking, they will teach that small is beautiful. Small pitches, small teams, small passes, even small players. The technical masters produced by Barcelona's La Masia academy are the inspiration for the next generation. On Friday night in Kiev was not about that, though. It was about big men, literally and figuratively. Big men up front, big men at the back. Big men in the dressing-room, big men under pressure. Big was the new small in the Olympic Stadium. And big turned out beautiful for England."
Dominic Fifield (Guardian): "There are two images that endure. The first is of an airborne Andy Carroll, his eyes fixed on the ball as it careers over in a delicious arc from the right flank and the white flash of gritted teeth, his jaw fixed, an indication of the power he is straining to summon from heaving neck muscles. Beneath him Andreas Granqvist winces, his shoulders hunched as if resigned to the reality that Sweden have been undone. He is diminished, shrunk in the striker's presence. The second, much later in the contest, is of Danny Welbeck pirouetting on his left leg and carefully clipping England's third beyond Andreas Isaksson with the instep of his right foot. There is surprise then dismay etched across Olof Mellberg's brow as his momentum carries him towards goal and the ball dribbles beyond the prone goalkeeper at his side. Where one finish felt brutal, the other is impudent. Almost silky. Yet both have dashed the idea that this England team are purely functional and, actually, rather blunt."
Finally, and rather amusingly, one Swedish tabloid had jokingly prepared what it called 'tomorrow's headlines today' - mocked-up back pages of our newspapers - in anticipation of a landslide victory for their team. Fortunately for England, their dreamt-up 5-0 scoreline remained just that - pure fantasy.