Full-back Dumbaya, 25, has agreed a deal until the end of the season after leaving troubled Portsmouth last week and 20-year-old centre-half Essam arrives from Gillingham on a two-and-a-half year contract.
Manager Richie Barker brought the duo in after Claude Davis joined Rotherham, while Kyle McFadzean is linked with a move to Bristol City.
Barker told Town's website: "Mustapha is a player we have monitored for a while and he was, in my opinion, their man of the match when we played Portsmouth last month.
"He is a very athletic individual who loves to go forward but knows that his first job in the team is to defend.
"He can also play in midfield and is a player quite a few clubs were keen to sign when Portsmouth released him. Fortunately he has chosen Crawley and we are delighted to have him here.
"We are delighted to have Connor at the club. He fits the template of players I want to work with. He is young with lots of potential and has a real appetite to learn and improve.
"Losing Claude Davis this week meant we had to strengthen this area of the team and we now have, in my opinion, four excellent central defenders."