Carroll powered a bullet header past Ben Foster to put the hosts 1-0 and he then scored an exquisite volley, watching James Collins' long ball down on to his right boot before firing home first time, to seal the win following Gary O'Neil's strike.
Carroll featured heavily in England's European Championship campaign, but a drop in form and fitness meant he was excluded from the latest World Cup qualifiers against San Marino and Montenegro, but he said: "I hope to play in every game for England but I've haven't been picked, so I've just got to work hard here at West Ham and hopefully I'll be involved next time."
Hammers boss Sam Allardyce underlined his desire to keep Carroll beyond the end of the season, when his loan is due to expire.
Carroll has struggled to live up to his billing, both at Liverpool and West Ham, as a £35million striker, but the way in which he terrorised Jonas Olsson at Upton Park was reminiscent of the kind of bruising display he used to put in every week for Newcastle.
The Gateshead-born hitman now hopes he has proved a few of his doubters wrong.
"I was putting myself about and got two goals, so that's what I like to think I'm about," he told West Ham TV.
"Obviously I like to score goals, so getting two shows that I've got it.
"I'm feeling good with the lads and everyone is coming together and we're playing well at home,
"It was a great win. The lads worked hard and I got my two goals and we got the three points, so it was a great day."
- Sports & Recreation