Skipper Harry Kane opened the scoring before half-time with Mason Mount doubling the advantage after the break as Gareth Southgate’s side made it two wins out of two in Group I.
Phil Foden came close to extending England’s advantage seeing a fine shot tipped onto the post as the Three Lions consolidated top spot in the table.
Next up for Southgate’s side is a Wednesday night Wembley assignment at home to Poland.
Meanwhile Ferran Torres struck a crucial goal as Spain secured a dramatic last-gasp 2-1 win away to Georgia.
The 2010 world champions, who have not lost a World Cup qualifying game in 28 years, were behind at half-time after Khvicha Kvaratskhelia fired the hosts ahead.
However, City winger Torres then slid in to draw Luis Enrique's side level before striker Dani Olmo scored a dramatic long-range stoppage-time winner in Tbilisi.
Elsewhere, Ilkay Gundogan played the full 90 minutes as Germany secured a hard fought 1-0 win away to Romania.
Serge Gnabry’s 16th minute goal proved enough to clinch all three points in Bucharest as Joachim Low’s side made it back -to back wins in Group J to sit joint top with Armenia.
However, there was frustration for Oleks Zinchenko and his Ukraine side as Finland forced an 89th goal to earn a 1-1 draw in Kiev.
Junior Moraes' 80th minute effort looked to have secured all three points for the hosts only for Teemu Pukki to convert a penalty a minute from time to ensure the points were shared in Group D with Ukraine having two points to date.