The visitors, on the other hand, were seeking a return to winning ways after forcing Atletico Madrid to a late 1-1 draw last week.
At Jesus Navas Stadium, the hosts almost gained an early lead through Claudia Pina in the seventh minute but she missed narrowly.
Before the half-hour mark, Coleman and Julia Karlernas came close for Sevilla but could not fire past goalkeeper Patricia Larque as she ensured Rayo forced a goalless draw at half-time.
After the break, the hosts continued from where they left off as Pina, Toni Payne and Coleman combined well to break the deadlock but the latter failed to beat Larque nine minutes after the restart.