More on KentOnline
Ebbsfleet face an FA Cup replay on Tuesday night after being held by lower-league East Thurock in the fourth qualifying round.
These sides drew here in National League South last season and there was nothing between them again.
Danny Kedwell had the ball in the net for Fleet but the goal was ruled out for offside.
Kedwell returned to lead the line for Fleet after missing last Saturday's trip to Macclesfield following the birth of his daughter, while Sam Magri was back in the team at right-back after returning from international duty with Malta.
Anthony Cook was handed only his second start of the season in midfield with Luke Coulson the man to make way. New signing Antonio German was named among seven substitutes.
There were three former Dartford players in the Rocks squad. James White and Max Cornhill both started but Lee Burns was left on the bench.
The lively Montel Agyemang hit one shot over and another straight at Nathan Ashmore in the opening stages, although Fleet twice went close in between.
Sean Shields, playing down the right, saw his low cross sliced over the bar by Ryan Sammons and from the corner which followed, Shields and Kedwell both had efforts blocked.
Dean Rance then stole possession in midfield and fed Myles Weston, whose deep cross from wide on the right was headed down by Kedwell but straight into the arms of Lidakevicius.
Jack Connors' cross from the left reached Rance but he missed his kick, before Weston stung Lidakevicius' palms from distance after Fleet had been passing the ball around patiently.
George Allen headed over from a corner for East Thurrock, then Shields cut in from the left and lashed a shot over.
The Rocks started to move the ball about nicely but they failed to get in behind the Ebbsfleet defence.
Kedwell thought he'd broken the deadlock in first-half injury time when he expertly headed Shields' deep cross back across Lidakevicius but an offside flag cut short the celebrations.
At the other end, Lewis Smith was convinced he should have been awarded a penalty after wriggling past two defenders but referee Gary Parsons instead blew for half-time to the fury of the home players.
Fleet dominated possession at the start of the second half but long-range efforts from Cook and Powell failed to worry Lidakevicius.
German was sent on for his debut just before the hour and the pattern continued of Ebbsfleet penning the home side back in their own half.
Magri swapped passes with Powell and burst into the area but failed to hit the target with a left-footed shot.
Weston made way for Luke Coulson in Daryl McMahon's second change but it was East Thurrock coming into the game more as time ticked by.
They hit the bar with a header when Ashmore flapped at a corner, then prolific striker Sam Higgins rifled over when sent through by striker partner Smith.
Smith tried his luck from all of 35 yards and his shot had Ashmore scrambling on its way over.
Ebbsfleet, with Danny Mills now on for Kedwell, won a free-kick 30 yards out and Powell hit the target when he stepped up but Lidakevicius plucked the ball out of the top corner.
Higgins looked certain to win it late on for East Thurrock when Sammons' long diagonal ball dropped at his feet in the box but Ashmore spread himself to keep Fleet in the cup.
East Thurrock: Lidakevicius, Sammons, Harris, Allen, Ekpiteta, White, Agyemang, Cornhill, Higgins, Smith, Honesty (Burns 86mins). Subs not used: Peddie, Belho, Boswell, Marlow.
Ebbsfleet: Ashmore, Magri, Clark, Bush, Connors, Cook (German 57mins), Rance, Powell, Shields, Weston (Coulson 69mins), Kedwell (Mills 75mins). Subs not used: McLean, Miles, Graham, Mambo.
Attendance: 669.