Gabriel Sava produced a string of fine saves as Mick Daly's late header cancelled out Ryan McBride's opener to earn Mick Cooke's side a point at the Brandywell.
The first chance fell to the hosts when Alan Byrne brought Michael Rafter down on the edge of the area after 10 minutes – the in-form Rory Patterson forcing a fine stop from Sava. The Candystripes went ahead after 30 minutes. After some good work on the wing, Simon Madden found Rory Patterson, whose powerful shot was tipped behind by Sava.
From the resultant corner, Ruaidhri Higgins' flick was met by Patterson, whose header was cleared off the line, but Ryan McBride was quickest to react and powered a header beyond Sava. Drogheda were restricted to half-chances with Declan O'Brien firing over after good work from Gavin Brennan, and substitute Thomas Crawley denying Paul O’Conor.
The Boynesiders, yet to register a League win in three outings, had Sava to thank for keeping the match finely poised at the break. The Italian was alert to Rafter's sharp turn and shot in the 43rd minute, and kept out Patterson twice and Higgins in a superb treble save in first-half stoppage time.
The visitors started brightly after the interval with replacement Eric Foley seeing a lot of the ball. But again it was City who created the better openings. Michael Rafter slid the ball through for Patterson after 63 minutes, but he was again thwarted by the onrushing Sava. Two minutes later Paul O'Conor spread a wonderful ball right, and made a marauding run to connect with the cross but Gerard Doherty was well down at his near post to keep out the header.
Derry should have made sure of all three points 15 minutes from time when substitute Thomas Crawley headed over the bar after finding himself well placed. But Drogheda salvaged a point when Mick Daly beat his marker at the near post to head past a static Doherty.