Forwards Haskell and Croft were particularly effective as England bossed possession, while Garvey scored with his first touch after coming on as a second-half replacement.
Harlequins' David Strettle wasted one early chance before Andy Vilk opened the scoring for England.
Haskell, the Wasps blindside flanker, then burst onto Simon Amor's pass and brushed aside Scotland's Murray Binghurst to score in the corner.
Amor created England's third try before the interval with a quick tap penalty and Ben Gollings provided Strettle with the scoring pass.
England continued in similar fashion after the break, when Strettle slipped two tackles, straightened and sent Bath's Nick Abendanon under the posts.
Garvey's gas left Binghurst standing and Croft rounded off the scoring late after Gollings linked with Haskell.
Head coach Mike Friday was satisfied by the start but insisted there will be plenty to work on, particularly in defence, if England are to retain their Dubai title.
"It was good in parts and all the debutants made a positive start," said Friday.
"It was obvious to see the guys hadn't played much Sevens before and there were still some naiveties, particularly in defence, that need adjusting as the tournament goes on.
"We are looking to grow as a team through the tournament, taking little steps in each match we play.
"The players were blowing a bit at the end, they haven't got their Sevens lungs yet."
England's next pool opponents were Zimbabwe, who pulled off a shock 19-7 victory over France.
In a repeat of last weekend's Test match at the Millennium Stadium, Wales could not live with New Zealand's pace and power as they fell to a 31-12 defeat.
The Kiwis bossed the breakdown and ran in five tries - but an inexperienced Wales side still retained hope of qualifying for the Cup competition from Pool D.
Aled Thomas created the first with a break down the right wing before finding Rhodri McAtee with the inside ball.
The second, a brave counter-attack from inside their own 22, was started and finished brilliantly by Cardiff's Tom James. Wales were on the back foot but James spotted an opening out wide and through a brave long pass to Aled Jenkins, who escaped down the right wing.
James raced on in support and received the pass back from Jenkins to score under the posts.
Thomas, the Dragons fly-half, said: "New Zealand were very strong at the breakdown both on their own ball and on our ball.
"Eight of the squad have not had a taste of Sevens at this level so we can take a lot of positives out of it which we can take on for the rest of the tournament and hope to qualify.
"We will certainly give it a good go."
Wales will need to overcome Samoa, who beat the Arabian Gulf 54-0 to clinch a place in the cup competition.
In surprise results, Portugal beat Australia and Tunisia edged Argentina.