Valeri Qazaishvili opened the scoring for the hosts after 10 minutes and Albania Under-21 international Rashica doubled their lead eight minutes later before Hakim Ziyech pulled one back for Twente on the stroke of half-time.
But second-half efforts from Chelsea loanee Dominic Solanke, Rashica's second of the match and a late score from Denys Oliynyk put the result beyond doubt for Arnhem to leave the visitors with just one win from their last eight matches.
