Jofra Archer and Mark Wood claimed three early wickets on the final day as the West Indies made a shaky start chasing 200 to win the first Test.
Second-placed City had lost their previous three away games but never looked likely to extend that streak against a Brighton side that struggled from the outset.
The Premier Soccer League season was one of a handful of competitions across the globe that was affected by the coronavirus pandemic
The win took second-placed Barca on to 79 points after 36 games, one behind Real Madrid who can restore their four-point advantage when they visit Granada on Monday.
Both handballs were clearly accidental but, under the current rules, referee Piero Giacomelli had no option but to award the penalties.
The West Indies hold a commanding 99-run lead over England at the end of the third day of the first Test on Friday.
Wimbledon, which was initially scheduled for June 29-July 12, was cancelled for the first time since World War Two due to the Covid-19 pandemic which has killed more than 44,000 people in the United Kingdom.
Norwich City have been relegated to the Championship thanks to a 4-0 hammering at the hands of West Ham United, where Michail Antonio scored all four goals.