The Imps had to settle for a point at Exeter as they stretched their unbeaten run to six games.
Bailey Cadamarteri and Jack Moylan came into the starting XI as head coach Michael Skubala made two changes from the last league game against Bristol Rovers.
The opening periods were closely contested, with Caleb Watts firing wide for the hosts after four minutes.
But the Imps also started brightly, with Sean Roughan threatening to send Cadamarteri through and only a great interception stopping the No.9 getting free.
And Paudie O’Connor did well to win a header after Pierce Sweeney had sliced a clearance, but was unable to direct the ball on target.
Moylan was next up for the Imps with a low shot after being set up by Ethan Hamilton.
The Irish midfielder was on the end of another flowing move after 25 minutes which was started when City won the ball back int he middle of the park. House, after a one-two with Cadamateri, sent through Moylan who went for power but saw his effort go over the bar.
A free-kick awarded following Jack McMillan’s foul on O’Connor out on the left wing. Moylan’s low delivery missed everyone - though Lewis Montsma was centimetres away from getting a toe on the ball for a flick - and needed Joe Whitworth to be alert to palm the ball away with both House and Cadamarteri lurking to capitalise on any mistake.
Set-pieces were again proving profitable for the Imps. A Roughan delivery from the right was well punched by Whitworth, but only as far as Jefferies who tried to place a side-footed finish into the bottom right corner but saw it roll agonisingly wide of the post.
The last chance of the half went the way of the Imps, with O’Connor flicking the ball just wide with a header from Roughan’s cross.
There was an enforced change for the Imps at the interval, with Ethan Erhahon coming on for O’Connor who had struggled with a knock in the closing stages of the first half. That necessitated a tweak in formation, with a switch to a back four.
City started the second period brightly, with Whitworth having to be alert to get to the ball before House just 30 seconds after the restart.
A Moylan corner led to a good opportunity after 49 minutes. Jefferies’ shot back into the ground bounced in front of Montsma who was able get a header in - though was unable to generate enough power to trouble Whitworth.
Whitworth was tested again when Moylan sent House away. House cut inside his man and got plenty of power on his effort, but it was straight at the home keeper.
The home side made a double change as Gary Caldwell looked to get back in control of the game. Demetri Mitchell, one of those introduced, was central to a good move with Jack AItchison on the hour mark which ended with Mitchell’s shot being blocked behind.
The Imps continued to create the better chances as Moylan jinked past a couple of players down the left before putting in a delivery where the ball just would not fall for Jefferies or Erhahon.
And a fizzing first-time cross from Jefferies, after 70 minutes, found House - his header had Whitworth scrambling but the ball came at him so quickly it was all he could do to ensure he connected with it.
City looked to take advantage of tiring home defenders, with Makama lifting a late counter-attack effort over.
The game became stretched in the closing stages as both sides looked to claim a dramatic late winner.
There were two late red cards shown to the home side. David Perkins, a member of Exeter's coaching staff, was shown the red card for witholding the ball to prevent an Imps throw-in, while Ryan Woods earned his second booking late in the game.
Imps:: George Wickens, Lewis Montsma, Paudie O’Connor (c), Sean Roughan, Tendayi Darikwa, Dom Jefferies, Conor McGrandles, Jack Moylan, Ethan Hamilton (JJ McKiernan, 90+2), Ben House, Bailey Cadamarteri (Jovon Makama, 64). Subs not used: Jamie Pardington, Ethan Erhahon, Dylan Duffy, Rob Street, Zane Okoro.
Exeter City: Joe Whitworth, Jack McMillan, Ben Purrington, Tristan Crama, Ryan Woods, Ed Francis, Jack Aitchison, Millenic Alli, Caleb Watts (Jay Bird, 56), Vince Harper (Demetri Mitchell, 56), Pierce Sweeney. Subs not used: Shaun MacDonald,Jack Fitzwater, Sonny Cox, Amani Richards, Jake Richards.
Referee: Thomas Parsons
Attendance: 5,950 (216 away)
