This is the first time ever a bowler has taken six wickets for no run in any international match.
Nepal won the match by 10 wickets, reaching 17 for no loss in 0.5 overs.
Earlier, the record belonged to Malaysian Mas Elysa, who had claimed six wickets for three runs from her 4 overs against China women in January this year.
The 24-year-old Anjali dismissed six batswomen -- all for nought -- in 2.1 overs as Nepal bowled out Maldives, who elected to bat, for just 16 runs from 10.1 overs.
Anjali's team-mate, Karuna Bhandari (2/4) took two wickets, while two batters were run out.
Eight Maldives batters got out without opening their account, while two made single-digit scores.
In reply, Nepal chased down the target in just five deliveries, reaching 17 for no loss.
Opener Kajal Shrestha remained not out on 13 while there were four extras (2 wide, 1 leg bye and 1 no ball).
The run chase lasted just seven deliveries, of which five were legal.
After the match, Cricket Nepal tweeted: "Nepal's Anjali Chanda bowling figure is best bowling figure in Women T20I surpassing Malaysian Mas Elysa's 6/3. Also best bowling in debut.
"Nepal's victory in 5 balls, however, is not the quickest victory as Rwanda and Tanzania had defeated Mali in 4 balls in July 2019."