Coventry City had to settle for a point against Barnsley at Sixfields after the Tykes twice came from behind to take a share of the spoils.
McQuoid put City ahead after just three minutes with a neat finish but Hourihane threaded a 20-yard free kick inside Sky Blues 'keeper Ryan Allsop's near post on the half hour.
Clarke then smashed home City's second after a set piece from Jim O'Brien to restore City's lead but Lita nodded home an untidy second leveller from close range on the stroke of half time.
City manager Steven Pressley named unchanged side to the one that beat Sheffield United 1-0 on Saturday.
The Sky Blues had an early scare though when John Fleck was dispossessed in City's final third by James Bailey whose through ball found Sam Winnall to put over the bar from ten yards out.
Just seconds later the Sky Blues were ahead when a short pass through to Josh McQuoid saw the striker shrug off Lewin Nyatanga and slide a cool finish past Tykes keeper Adam Davies.
It was nearly two after seven minutes when a corner delivery from Danny Swanson picked out an unmarked Andy Webster to power a header just over the bar.
City were in fact overwheklming the visitors in the opening stages and went close again three minutes later when a ball over the top picked out Jim O'Brien who fired on the half volley and watched the ball head for the near top corner until it was beaten away by Davies.
Former Sky Blue Martin Cranie was then required to make a goal line clearance after Jordan Clarke's looping header from the resulting corner threatened to drop under the bar.
O'Brien went close again two minutes before the half hour when he stepped up to take a free kick from nearly 30 yards and clipped the crossbar with Davies beaten at full stretch.
The visitors were level out of nowhere two minutes later though with a free-kick of their own. Conor Hourihane curled a dead ball around the wall and threaded it inside Ryan Allsop's near post.
Hourihane nearly got a second soon after when confusion in teh City box allowed him to slip in, only to be denied by a point blank save from Allsop.
The Sky Blues restored their lead two minutes before the break though and deservedly so. Marcus Tudgay was brought down outside the area which allowed O'Brien to swing a delivery in the box. Andy Webster and Reda Johnson pressured the ball which eventually fell loose to Clarke who blasted home from five yards out.
The drama of the first half was not finished though as Hourihane whipped a corner ball into City's area on the stroke of half time to allow Lita to nod an untidy leveller while standing just a yard offf the line.
City seemed to overcome the disappointment of the equaliser after the break wjhe, seven minutes after the restart, O'Brien's corner found Clarke to head at goal only to be denied as Davies clawed the ball off the line.
McQuoid was then inches away from his second when Johnson swung in a cross from the left and the striker connected with a diving header that rose just over the bar.
The Northern Irish international almost could not believe his luck on 55 minutes when a mix up between Reece Brown and Joe Dudgeon let the striker in but Davies was quick off his line to make a point blank stop with his body.
Johnson then went close with a glancing header with 20 minutes to go and Ryan Haynes also drew a last ditch block from Reece Brown five minutes later.
New Sky Blues signing Simeon Jackson was introduced with 11 minutes to go to make his debut for the club although the cameo could not mark any dramatic winner as both sides saw out four minutes of added time to take a point each.
Attendance: 2,376 (883 away)
Coventry City: Allsop, Willis, Webster, Johnson (c), Clarke, Haynes, O'Brien, Swanson (Daniels 79), Fleck, Tudgay (Jackson 79), McQuoid (Miller 63)
Subs: Burge (GK), C Thomas, Coulibaly, Phillips
Barnsley: Davies, Brown, Dudgeon, Berry, Nyatanga, Cranie (c), Treacy (Digby 63), Hourihane, Winnall (Hemmings 89), Bailey, Lita (Cole 63)
Subs: M'Voto, Abbott, Dibble, Bree