Jobi McAnuff went closest for the O’s when his first-half free-kick came back off the crossbar. Forward pair Dan Holman and Macauley Bonne also had late second-half chances but couldn’t convert.
Head Coach Justin Edinburgh made four changes to the side that were defeated at home to Torquay United on Saturday afternoon.
Joe Widdowson, Jobi McAuff, Dan Holman and Matt Harrold come in to the side in place of Jake Caprice, Macauley Bonne, Lamar Reynold and David Mooney.
Orient drew 1-1 with Eastleigh in the reverse fixture back in August, when an injury time Craig Clay equaliser secured a home point for the O’s.
Eastleigh got the game underway in very cold Hampshire conditions and had the first chance of the game when Mark Yeates’ early effort took a deflection and rolled in to the hands of Dean Brill.
Jobi McAnuff sent a searching 25-yard free-kick in to the box, but central defensive pairing George Elokobi and Josh Coulson both failed to connect with the cross.
Yeates proved to be an early danger man for the hosts, as he saw two efforts from range whistle inches passed the post.
After 25 mintes, Brill punched clear a Gavin Hoyte cross, but only to Sam Wood on the edge of the box who fired just wide of the target.
Nine minutes of the first half remained when McAnuff clipped the bar from a 20-yard free-kick, Matt Harrold attempted to nod the rebound in but Eastleigh managed to clear as the first half ended goalless.
Eastleigh had two early second-half chances when Ben Williamson and Mark Yeates failed to make chances pay after latching on to the end of the ball inside the box.
Orient came close to the opener when Matt Harrold flicked the ball in to the path of Dan Holman whose shot was somehow excellently saved by Graham Stack in the hosts net.
Minutes later, newly introduced Josh Koroma got the better of his marker and drilled a low cross into the box but it missed everyone and was cleared by Eastleigh.
Koroma was involved again after he forced his way in to the box and laid off Bonne who struck at goal but saw a deflection take the effort wide.
Orient were certainly in charge of possession when a rare Eastleigh chance saw Sam Matthews strike from range but the effort was high and wide of the target.
Bonne went close at the death when he headed just wide from Jame Brophy’s cross as the game ended 0-0.
EASTLEIGH: Stack, Hoyte, Togwell (C), Johnson, Wood, McCallum (Zebroski 79), Yeates, Obileye, Boyce, Miley (Matthews 68), Williamson
SUBS: Cresswell, Broom, Hollands
BOOKED: Johnson (35), Hoyte (45), Obileye (88), Togwell (88)
ORIENT: Brill, Widdowson, Elokobi, McAnuff (C) (Koroma 53), Coulson, Clay, Brophy, Harrold, Holman (Bonne 61), Adams, Ling
SUBS: Grainger, Mooney, Ekpiteta
BOOKED: Adams (72)
REFEREE: Joseph Johnson
ATTENDANCE: 2,013 (453 Orient supporters)