Robert Bayly produced a stunning late equaliser to cancel out John Flood's strike and deny Drogheda United victory at Tallaght Stadium.
Drogheda keeper Paul Murphy had earlier kept out a half-volley from Bayly but could do nothing to stop his low drive on 82 minutes.
Drogheda are a side transformed under new manager Darius Kierans and will feel they deserved their point. They put in a spirited performance that belied their lowly position in the table.
However, they will rue a lapse in concentration that meant Bayly was not closed down before he struck the equaliser.
It was a game full of chances and excitement, but a combination of poor finishing and fine goalkeeping meant both teams had to settle for one goal apiece.
Rovers will be disappointed not to have won as they had enough chances to win three games. The point means that the Hoops slip behind St Patrick's Athletic in the title race as they head into the mid-season break.
Thomas Stewart replaced Sean O'Connor on the left for Rovers as the home side went with an attacking line-up from the start.
Kierans made two changes to the side that lost to UCD in the cup. Murphy replaced Paul Skinner in goal and Paul Crowley returned from suspension in place of Ryan Brennan.
Drogheda settled well and good approach play yielded an early chance for Mick Daly, but he shot straight at Alan Mannus from the edge of the box.
James Chambers was the first to go close for Rovers when his free-kick hit the base of the post after Joey Kendrick had fouled Gary Twigg.
Twigg was the next to try his luck for the home side after Stewart's cross deflected into his path, but the snap shot drifted wide.
Drogheda were certainly not playing like a side struggling in the league and Gareth O'Connor and Paul Crowley had chances to test Mannus, but neither could force a save from the keeper when well placed.
Another Stewart centre caught out Eoghan Osborne, but Chambers could not capitalise on the full-back's error.
Drogheda were grateful to Kendrick for keeping the game scoreless on the half hour when he denied Dessie Baker a clear shot on goal after a sweeping Rovers move involving Stewart, Bayly and Twigg.
Danny Murphy then produced a great cover challenge on Flood as he raced away from Craig Sives and Dan Murray. There was a further scare for Rovers moments later, as Mannus pushed away Kendrick's curling free-kick.
The second half picked up where the first half left off and Rovers should have taken the lead moments after the restart in an incident reminiscent of the Keystone Cops.
A slip by Alan McNally let in Baker who fed Twigg and he picked out the unmarked Chambers. However, Chambers screwed his shot across goal to Baker, but he could not keep his effort beneath the crossbar.
At the other end, Flood gave Rovers a warning of things to come when he ghosted in unmarked, only to head straight at Mannus.
Rovers then laid siege to the Drogheda goal and Murphy produced a stunning save to keep out Bayly's half-volley. From the resulting corner, Twigg blocked Stewart's goal-bound effort.
However, it was Drogheda that went ahead on 67 minutes through Flood. O'Connor raced forward and fed the striker, who calmly slipped the ball beyond Mannus.
Brendan McGill should have doubled his side's lead minutes later after another through ball from O'Connor, but the winger's shot was weak and easily saved.
With 15 minutes remaining, Michael O'Neill introduced Billy Dennehy for defender Pat Flynn as Rovers went for broke chasing the equaliser.
The gamble paid off as Bayly's long-range daisy-cutter skidded past Murphy on its way into the corner.
Both sides could have won at the death as Sives hoofed away Ryan Brennan's low cross from his own line and Twigg scuffed a shot straight at Murphy.
Shamrock Rovers: 1 Mannus; 13 Flynn (20 Dennehy '74), 4 Sives, 24 Murray, 19 Murphy; 6 Rice (18 Turner '60), 25 Bayly, 8 Chambers; 10 Baker, 23 Stewart (17 O'Connor '68), 22 Twigg.
Subs not used: 14 Barrett, 16 Duggan.
Drogheda United: 23 Murphy; 2 Treacy, 5 McNally, 3 Kendrick, 12 Osborne; 6 E McGill, 10 Crowley (19 Brennan '87), 16 Daly, 7 B McGill; 11 Flood (8 Duffy '84), 14 O'Connor.
Subs not used: 1 Skinner, 18 Fitzpatrick, 20 Smyth.
Booked: Daly, O'Connor, Murphy
Referee: Neil Doyle