While Roy Hodgson's team were going through the motions of a 5-0 victory over San Marino at Wembley, the Swiss, already beaten at home by England in their opening game, went down 1-0 in Slovenia.
Thursday's results left England and Lithuania on top of the group with six points, while Estonia and Slovenia have three.
If Switzerland's defeat was something of a surprise, Hodgson told reporters that with Spain also losing on Thursday against Slovakia, results could not be taken for granted against teams a level above the real minnows like San Marino.
"We should stop being surprised these days in international football," he said.
"I don't think we can just expect that because you happen to be called Switzerland or Spain or Russia or England you're going to beat whoever you play because they don't have so many people living in their country,” he added.
Nevertheless, England fans will expect exactly that on Sunday against a team who have never reached the finals of a major championship.
England have no new injuries ahead of Sunday's game, and once they were 2-0 ahead on Thursday, Hodgson took off Liverpool's Jordan Henderson and Raheem Sterling at halftime, and Arsenal striker Danny Welbeck later.
All three are expected to start again in Tallinn, where Hodgson's only concerns will be any complacency among his squad and how few training sessions can be fitted in.
"We have very little preparation time," he said.
That lack of training pitch time no doubt contributed to Hodgson's decision to persist with his diamond formation in front of a regulation back four on Thursday, despite England facing a side with virtually nil attacking threat.
It made for largely insipid viewing in a half-empty, virtually silent Wembley and Hodgson and his players will just be pleased to have put the game behind them.
Estonia should be another straightforward assignment in a qualifying group that already looks done and dusted for England after only two rounds, though they are certainly a step up from hapless San Marino.
England and Estonia have met twice before, in qualifying for the 2008 European Championship, when England won each game 3-0.

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