Some restrictive bowling from Sian Ruck, Lucy Doolan and Watkins helped carry the White Ferns to a hard-fought 10-run win in their group match at Warner Park in Basseterre, St Kitts today.
India reached 129 for eight from their 20 overs, unable to overhaul New Zealand's 139 for eight, headlined by 32 off 30 balls from opener Suzie Bates.
However, Watkins said improvements would be needed if they were to be a force at the eight-nation tournament and wanted to see it in their remaining group matches against Sri Lanka on Sunday (NZT) and Pakistan on Tuesday, both at Basseterre, with the top two teams advancing to the semifinals.
"We'll take the win but it definitely wasn't a complete team performance," Watkins said.
"There were a few players making starts with the bat and not going on. We ended up losing wickets instead of batters going on to get 60s and 70s.
"Also, with the ball our seamers need to make some real improvements in the games coming up.
"The wickets are good batting pitches so the margin for error is pretty small. We'll be working on hitting our yorkers on training and making sure we're not varying in length."
The Indians made a bright start courtesy of 28 from opener Sulakshane Naik and 44 from Mithali Raj but Raj's dismissal left India teetering at six for 91 with less than five overs remaining.
Left-arm seamer Ruck bowled through her four overs at the top of the chase and took two for 17 while her Wellington teammate Doolan nearly matched those figures, taking two for 18 off four with her offspin.
Watkins contributed to India's mid-order mailaise with one for 23.
New Zealand's own innings lacked momentum, failing to take advantage of the base laid by Bates, the hard-hitting opener who Watkins singled out as a key figure.
"She was disappointed to get out for 32... but she's one of those players who can win a game single-handedly. Making sure she's in form and fit right through the tournament is going to be important for us."
Nicola Browne and Rachel Priest were the best contributors with knocks of 24 off 17 balls and 20 off 12 respectively.
Today's other match from the same group saw Sri Lanka beat Pakistan by one run.
