Sevilla moved on to 45 points from 21 games, four points behind Real Madrid and eight ahead of Betis in third. Champions Atletico Madrid are fourth with 33 points.
Sevilla went ahead early in the first half with an own-goal from Mouctar Diakhaby. The French defender tried to clear a cross from Gonzalo Montiel directed to Lucas Ocampos and diverted the ball into Jasper Cillessen's net.
Valencia equalised just before halftime with an opportunist header by Goncalo Guedes from the edge of the six-yard box.
Valencia defender Jose Gaya, who had a goal disallowed for offside, was sent off in the 88th minute for a strong challenge on Ocampos.
"We knew that it wasn't going to be easy play here, we had many opportunities and didn't take advantage. We will have to accept this result and go back home with one point," Sevilla defender Karim Rekik told reporters.
After a high-paced first half, in which Valencia keeper Cillessen went off injured, the game dropped in intensity.
New signing Jesus Corona was sent on midway through the second half and sparked life into Sevilla with a couple of good attempts on goal but Valencia held on for the draw.