Sportal.co.nz 03.Feb.2013Getty Images
Gloucester centre Twelvetrees impressed on debut, one of four players to cross for England at Twickenham on Saturday.
Chris Ashton, Danny Care and Geoff Parling were the other try scorers, while Owen Farrell contributed 18 points with the boot in his strong performance.
Farrell put England on the board after just two minutes before Scotland took a surprise lead.
New Zealand-born winger Sean Maitland, also on debut, helped Scott Johnson's side capitalise on a poor Mike Brown kick, crossing in the corner.
England reclaimed the lead through consecutive Farrell penalties before Greig Laidlaw reduced the deficit with a three-pointer of his own.
But it was all England from then on as Ashton crashed over for his 17th Test try in the 30th minute and his team took a 19-11 lead into the break.
Scotland continued to give away penalties and when Twelvetrees and Parling crossed, England had one hand on the Calcutta Cup.
Stuart Hogg scored a consolation try before Care got England's fourth as they eased to the win.
Reigning champions Wales slumped to their eighth straight loss, beaten 30-22 by an impressive Ireland at Millennium Stadium.
Wales achieved their third grand slam last year but have been in poor form, and it continued in Cardiff.
Ireland rushed to a 30-3 lead on the back of tries from Simon Zebo, Cian Healy and Brian O'Driscoll, as well as 15 points from Jonathan Sexton.
Conor Murray and Rory Best were sin-binned for Ireland in the second half as Wales added respectability to the score-line with Alex Cuthbert, Leigh Halfpenny and Craig Mitchell crossing.