Coventry captain Robert Page earned his side a point after heading in from a corner with five minutes left.
The Sky Blues almost took the lead in the third minute after a defensive mix-up in the Reading box.
After good work down the left by Gary McSheffrey, Royals goalkeeper Marcus Hahnemann came to collect the cross but, not hearing the call, centre-half Ibrahim Sonko sliced the ball over the bar.
But Reading had the better of the opening exchanges and their first real chance to score came in the 15th minute.
A long ball over the top by captain Graeme Murty saw Kevin Doyle out-sprint both Marcus Hall and Richard Shaw but his shot was saved by Bywater.
The pace of Lita always caused Coventry problems and the former Bristol City man saw his shot saved by Bywater soon after.
Reading should have taken the lead in the 24th minute when Byrnjar Gunnarsson put a free header over the top.
A quickly taken free-kick saw Glen Little put in a delightful cross to the unmarked Gunnarsson who should have done better.
A minute later a lovely move between McSheffrey, Hall and Dele Adebola saw Coventry's top scorer turn and shoot but his shot came back of the upright.
McSheffrey retrieved the loose ball and his cross saw James Scowcroft's header go straight into the grateful arms of Hahnemann.
The game burst into life in just before half-time when Reading were awarded a penalty after Coventry captain Page was adjudged to have pushed Doyle in the box.
Lita put his spot-kick to the right of Bywater but his shot was magnificently saved.
Coventry went straight down the other end and Adebola threaded the ball through to Scowcroft but his shot was saved well by Hahnemann.
Reading again started the better in the second half and made the breakthrough in the 68th minute after some sloppy Coventry defending.
Doyle was allowed to collect a Little throw-in and turn and run into the Coventry box. His first shot was saved by Bywater but the on-loan West Ham keeper was helpless to stop him putting in the rebound.
But Page headed home with five minutes remaining from a McSheffrey corner to give his side a well-deserved share of the spoils.