Wrexham had the best of the first half, but could not break down a stubborn Spitfires defence.
Eastleigh goalkeeper Ross Flitney saved at John Rooney's feet and substitute Callum Powell saw his curling shot go just wide.
The game petered out after the break, with an injury to defender Curtis Tilt a concern for Wrexham boss Gary Mills.
Wrexham manager Gary Mills: "I thought we were excellent today, different class. Excellent at the back, excellent in midfield, excellent. I loved watching my lads today.
"It is a good point against a good side, but we were the better team. The players want to play for each other."
Match ends, Wrexham 0, Eastleigh 0.
Second Half ends, Wrexham 0, Eastleigh 0.
Substitution, Wrexham. Nortei Nortey replaces Mark Carrington.
Substitution, Eastleigh. Mikael Mandron replaces Jai Reason.
Substitution, Wrexham. Tyler Harvey replaces Curtis Tilt.
Substitution, Eastleigh. Yemi Odubade replaces Adam Dawson.
Substitution, Eastleigh. James Constable replaces Ryan Bird.
Second Half begins Wrexham 0, Eastleigh 0.
First Half ends, Wrexham 0, Eastleigh 0.
Substitution, Wrexham. Callum Powell replaces Michael Bakare.
First Half begins.
Lineups are announced and players are warming up.
Eastleigh earned a point in new manager Ronnie Moore's first game in charge after taking over from Chris Todd.