Sam Matthews stunned the home crowd early on from long range, but Aswad Thomas replied quickly for Dover.
The irrepressible Miller then went out on his own at the top of the scoring charts, notching a quick-fire hat-trick. The second was a real highlight as he wormed his way inside from the corner flag before beating Joe Taylor.
Jack Parkinson made it five before half-time from close range. The break helped Braintree steady matters, and Dover's rampant form subsided.
But Miller grabbed his 14th of the season from a free-kick to cap his perfect day.
Reports supplied by the Press Association.
Match ends, Dover Athletic 6, Braintree Town 1.
Second Half ends, Dover Athletic 6, Braintree Town 1.
Substitution, Dover Athletic. Ira Jackson Jr replaces Ricky Modeste.
Substitution, Braintree Town. Joe Maybanks replaces Sam Matthews.
Substitution, Dover Athletic. Mitchell Pinnock replaces Ricky Miller.
Substitution, Dover Athletic. Ayo Obileye replaces Tyrone Sterling.
Jon Ashton (Braintree Town) is shown the yellow card for a bad foul.
Substitution, Braintree Town. Jack Midson replaces Harry Lee.
Sam Matthews (Braintree Town) is shown the yellow card for a bad foul.
Substitution, Braintree Town. Jon Ashton replaces Barney Williams.
Goal!  Dover Athletic 6, Braintree Town 1. Ricky Miller (Dover Athletic).
Second Half begins Dover Athletic 5, Braintree Town 1.
First Half ends, Dover Athletic 5, Braintree Town 1.
Goal!  Dover Athletic 5, Braintree Town 1. Jack Parkinson (Dover Athletic).
Goal!  Dover Athletic 4, Braintree Town 1. Ricky Miller (Dover Athletic).
Goal!  Dover Athletic 3, Braintree Town 1. Ricky Miller (Dover Athletic).
Goal!  Dover Athletic 2, Braintree Town 1. Ricky Miller (Dover Athletic).
Goal!  Dover Athletic 1, Braintree Town 1. Aswad Thomas (Dover Athletic).
Goal!  Dover Athletic 0, Braintree Town 1. Sam Matthews (Braintree Town).
First Half begins.
Lineups are announced and players are warming up.

Hundreds of witnesses have given testimony to the inquiry that has been examining allegations of historical abuse and neglect.
A report is expected next year.
The HIA was set up in 2013 to investigate child abuse in residential institutions in Northern Ireland over a 73-year period, up to 1995.
Analysis - BBC News NI's Kevin Sharkey
Men and women who were vulnerable children in care in Northern Ireland between 1922 and 1995 have appeared before the inquiry to give accounts of their childhood abuse.
Now middle-aged or elderly, they travelled to Northern Ireland from across the UK and Ireland.
Many others gave evidence from around the world, particularly from Australia.
Now they must all wait until the final report is given to politicians at Stormont, six months from now.
Ministers will then decide how to respond to a number of issues, including compensation.
These included a range of institutions, run by the church, state and voluntary sector.
It has been led by retired judge Sir Anthony Hart.
Ricky Miller scored four times in Dover's 6-1 win over struggling Braintree at the Crabble Athletic Ground.
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Public hearings at the Historical Institutional Abuse Inquiry (HIA) come to an end on Friday after two and a half years.