The Imps struggled for the first hour and looked to be heading for an opening day defeat until Birch got on the score sheet in the 64th minute.
Northampton keeper Lee Harper did well to push out a header from Derek Asamoah but could only watch as his defenders hesitated leaving Birch to scramble the ball home from six yards.
The goal seemed to wake up Lincoln and four minutes later Francis Green almost snatched a winner. The former Peterborough striker broke through the middle only to be stopped by a tremendous tackle from Luke Chambers.
Lincoln kept up the pressure until the final whistle but the Northampton defence held out.
The late burst by Lincoln was in contrast to the opening 60 minutes when Northampton dominated.
Town fully justified their label as the bookies favourite for the League Two title and should have had the game sown up.
A dangerous cross from Josh Low skidded off the shins of Lincoln defender Jamie McCombe and spun across his own goal.
The resulting corner from David Hunt found Pedj Bojic at the near post but his effort was well held by Lincoln keeper Alan Marriott.
Then Low got in a powerful shot in first half stoppage time but his effort was deflected wide.
Low created plenty of problems for Lincoln and in the 48th minute he fired an excellent ball into the box. The Lincoln defenders were caught out but Eric Sabin was just unable to make contact.
Northampton's opener came in the 53rd minute when Bojic ran unchallenged towards goal. Four defenders backed off allowing him to pick his spot leaving Marriott helpless with his 20-yard shot.
Four minutes later Low created a half chance for Sabin, but the big striker's shot was held by Marriott. Eoin Jess and Low combined to create an opening for David Galbraith but the midfielder saw his header saved.