Having won the first Twenty20 international by eight wickets on Wednesday, England coasted to a nine-wicket victory in less than 10 overs at Hove.
The tone was set with the ball by Arlott, who only made her international debut in the first match and took 3-14 from her four overs.
After bowling West Indies captain Hayley Matthews for six, Arlott snared Zaida James with the help of a brilliant catch from Sophia Dunkley before sending Stafanie Taylor back for a duck.
Arlott also took a catch as England impressed in the field, while Lauren Bell claimed three wickets and Charlie Dean two in the Windies' paltry total of 9-81.
Danni Wyatt-Hodge was bowled by James off the first ball of England's reply but it was a minor blip as captain Sciver-Brunt led the home side to victory.
She smashed an unbeaten 55 off only 30 balls while Dunkley played the supporting role with 24no as England reached the required total off only 9.2 overs.
Arlott was named player of the match, and she told Sky Sports: "Obviously it's kind of a dream start to my career with England.
"It's nice to get back to winning ways with the girls. I thought we were great as a unit today. I think everybody really stood up and did a job. It's a great group of girls, they've been great to welcome me in."
Sciver-Brunt was full of praise for Arlott, saying: "The bowlers set up the game beautifully today, made great use of the power play, and, when you've got someone who's two games into their career begging me to bowl four overs straight through, it's a dream."
England will try to complete a 3-0 series sweep at Chelmsford on Monday.
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