Jennings comes in for opening batsman Hameed, set to return home for surgery on his badly-broken left little finger, and Dawson takes the place of Ansari while the latter continues to struggle with the back injury which ruled him out of the third-Test defeat in Mohali.
Johannesburg-born Jennings appears set to become captain Alastair Cook's 11th opening partner, since the retirement of Andrew Strauss four years ago, when the series resumes in Mumbai next week.
The 24-year-old son of former South Africa coach Ray Jennings had a breakthrough summer in which he was the leading run-scorer in the Specsavers County Championship - amassing almost 1600 at an average of 64.50 in Division One for Durham.
He will make his England Lions debut against United Arab Emirates in Dubai on Thursday, and then has a tough act to follow after Hameed earned a band of new admirers with his wonderfully-skilled and brave rearguard half-century - down at number eight because of his injury - as England nonetheless lost by eight wickets on Tuesday to go 2-0 down with two to play.
Hampshire all-rounder Dawson, like Ansari a left-arm spinner, is currently busy at the Bangladesh Premier League with Rangpur Riders.
Ansari, meanwhile, will stay with the squad and continue to receive medical support in India before returning to England on December 8 - day one of the Mumbai Test.
Jennings is due to join up with England in Mumbai on December 5, after much of the rest of the squad return from a short mid-series break in Dubai
Neither he nor 26-year-old Dawson has previously figured in a Test squad, although the latter made both his one-day international and Twenty20 debuts last summer.
He too is expected to arrive in Mumbai early next week.