Try doubles by skipper Martin Corry and wing Paul Sackey - plus 24 points from fly-half Jonny Wilkinson on his first start in the tournament - saw England home 44-22.
But they were given a major fright as Samoa hauled themselves back to 26-22 adrift after trailing by 17 points just before half-time.
Scrum-half Junior Polu's try - awarded following lengthy deliberation by the video referee - and five penalties and a conversion from full-back Loki Crichton kept Samoa firmly in the hunt.
England though, finished in style as Corry and Sackey posted late tries to set up an intriguing Parc des Princes showdown.
Australia are likely to await the winners in next month's opening quarter-final.
Head coach Ashton said: "We played with a bit more shape and balance than in the previous two games (against USA and South Africa).
"When Samoa got back to 26-22, our defence held up pretty well.
"But we have still got a hell of a lot of hard work to do. Both teams have a six-day turnaround, and it is going to be a fight to the death on Friday night.
"This was a step in the right direction. Hopefully, it will give the whole squad a boost of confidence that can show the way to better things.
"At 26-22, the game could have gone either way, but we grasped it again by the scruff of the neck and scored two tries in the end.
"I thought there was a lot of courage in the performance."
Corry set the tone by crashing over after just 79 seconds, yet it was Wilkinson's kicking - four penalties, two drop-goals and three conversions - that kept England ticking over.
His latest haul took him past 200 World Cup points, a feat only previously achieved by Scotland's Gavin Hastings.
Corry said: "We are pleased, but we are not going overboard. We knew this was always one of two games for us, and there is another big game next week.
"It has been knock-out rugby for us since we lost to South Africa.
"We've been through so many emotions as a squad since the South Africa game."