The result sets up a tantalizing clash with France, who beat Poland 3-1 earlier in the day, for Gareth Southgate's side in the two European heavyweights' first-ever knockout round meeting at a World Cup.
"The ruthlessness of the performance was excellent," Southgate said after the match. "Every match you play is a different sort of challenge and different tactical problem to resolve. We've stepped up and are answering those questions.
"The quality of the moves was outstanding and the finishing was ruthless."
Jordan Henderson and captain Harry Kane both scored just before the break to secure a 2-0 half-time lead against a Senegal side that had looked entirely up to the task at Al Bayt Stadium in Al Khor, Qatar.
Speedy Senegal striker Boulaye Dia, who looked dangerous on the counter, came closest for the African side when he brought out a sharp one-handed save from Jordan Pickford after England's defence carelessly gave the ball away just past the half-hour.
"Really tough. Knockout games are never easy," said man of the match Kane. "We've shown great maturity through the tournament ... 3-0 here against a really good side. Mentality was top from the beginning and we took our chances when they came.
"We feel good, we've got good players getting forward and we're solid at the back. A really good day for us."
Henderson settled England's nerves in the 38th minute, stroking the ball home after being played in by Jude Bellingham at the end of a lovely passing move.
Kane struck a ferocious shot past goalkeeper Edouard Mendy with the last kick of the first half, leaving him one goal behind Wayne Rooney's record of 53 goals for England.
Manager Aliou Cisse rang the changes for Senegal at half-time but to little effect, as Bukayo Saka put England three up in the 57th minute, applying a deft touch to Phil Foden's cross through the 6-yard box over the outstretched arms of Mendy.
"We have worked for years to be African champions but now we were up against one of the top five teams in the world and I think you saw the difference tonight," Cisse said. "We were playing a very good England team and you saw that in the challenges and their physical strength.
"Plus we weren't as good as we should have been."
Saka's strike took England's total goals thus far in Qatar to 12 -- level with the country's World Cup record number scored in reaching the semifinals in Russia -- as the Three Lions saw out the match at a canter.
"We all want to play in the biggest games and no better game than playing France," Foden said. "On our best game we can create chances and score, were looking forward to what's going to be a big challenge."
The victory extended England's all-time unbeaten run against African teams to 21 games, including eight in World Cups. Morocco, who face Spain on Tuesday, are now the only African team left in the tournament.
The absence of the suspended Idrissa Gueye and injured Cheikhou Kouyate left Senegal's midfield too underpowered to pose problems for England.
With Sadio Mane missing the tournament through injury, Senegal also lacked a cutting edge to trouble an England defence that kept a third successive World Cup clean sheet for the first time in 20 years.
"I said throughout the tournament his absence was a blow to us. It is tough when you lose a player like that," Cisse added.