Andy Murray hailed his “perfect start to the grass season” as the three-time Grand Slam champion stepped up preparations for Wimbledon in style.
Purcell rallied from a set down to beat De Alboran 5-7, 7-6, 6-4 in a final that lasted over three hours.
Nagal entered the tournament through the qualifying rounds, whereas Jung entered as a lucky loser.
The 36-year-old British player lost in the 2016 final to Novak Djokovic and reached four other semifinals at Roland Garros in western Paris.
It took Nagal an hour and 22 minutes to secure a 6-1 6-4 win over Jay Clarke of Great Britain.
Nagal posted a 6-1, 6-3 win over Ji Sung Nam while Mukund stunned Jason Jung, the No.1 seed, in the qualifying, 4-6, 6-4, 6-4 to book their spots in the main draw.
Duckworth did not have to strain himself much to win the first set, but it was Purcell, who rallied to win 3-6 7-5 7-6 (5) in the final.
Former top-10 professional tennis player Fernando Verdasco accepted a voluntary provisional doping suspension of two months after testing positive for a medication for ADHD.
Verdasco said he was taking methylphenidate as a medication prescribed by his doctor to treat ADHD.