Afghanistan failed to clinch key moments in the games and with Rashid not enjoying a fruitful campaign, Afghanistan struggled at the big stage.
Despite the victory, two-time former champions West Indies remain second-bottom of the 10-team table and will slink home with just two wins from nine matches.
Afghanistan allrounder Mohammad Nabi's 52 gave India a proper scare at The Ageas Bowl.
Virat Kohli made 67 and Kedar Jadhav 52 as India struggled to dominate Afghanistan.
Tahir ended with figures of four for 29 in his seven overs, while Morris returned with exquisite numbers of three for 13 in his 6.1 overs.
Relive all the action in pictures from Bristol where defending champs Australia opened their ICC World Cup 2019 account with a seven-wicket win over Afghanistan.
Afghanistan's total of 207 all out, made following captain Gulbadin Naib's surprising decision to bat first at Bristol on Saturday, never looked like troubling.
Australia will be firm favourites to knock off the runs in the fourth match of a tournament characterised by one-sided contests so far.
Ireland never looked likely to threaten Afghanistan's total despite Paul Stirling's 56-ball half century – his fourth successive score of 50 or more.
Simmons, who took up the position in December 2017, said that the time is right for him to move on after accomplishing his goal – to help Afghanistan reach the World Cup.