The Shire belied their status as basement battlers and kept Jim Chapman's men at bay in the first half.
Ryan McStay cleared Ross Fisher's header off the line, while Thomas Orr got on the end of a pinpoint cross, but headed just over the bar.
Despite Shire's bright start to the second half, Annan led when Todd flicked home Ben Jago's long shot.

The DUP says up to 90% of the PSNI legacy investigation branch's caseload is focused on killings by the Army.
The PM, secretary of state and other unionist and Conservative politicians also say there is an imbalance.
But PSNI figures show investigations into killings by the Army account for about 30% of its legacy workload.
The police legacy branch will re-investigate 1,118 deaths not previously reviewed or completed by the now defunct Historical Enquiries Team (HET).
Of those killings, 530 were carried out by republicans, 271 by loyalists and 354 by the security forces.
It is not known who was responsible for the other 33 killings.
Team A consists of 12 detectives
They are working on On The Runs (OTR) enquiry and are seeking to confirm the "wanted" status of 228 republicans, not all of whom received OTR letters.
The number of incidents the individuals are linked to may run to several thousand.
The team is examining whether there is evidence that would provide grounds for them to be prosecuted.
Team B consists of 19 detectives
Its caseload includes investigations into the killings of Jean McConville and former IRA member Eamon Collins, both attributed to republicans.
The team is also investigating the activities of the Military Reaction Force (MRF).
Team C consists of 13 detectives
They are investigating the killings of 13 civilians by members of the Parachute Regiment on Bloody Sunday, and the murders of 10 Protestant men by the IRA at Kingsmills in 1976.
Team D consists of 11 detectives
It is investigating seven killings by republicans.
The officer who leads the PSNI legacy branch, Assistant Chief Constable Mark Hamilton, said he did not believe the police were disproportionately focusing on any one group.
"I do understand that there is a public perception that there is a disproportionate focus on military cases but they form part of what we are doing," he said.
"I have a full team who are doing reviews against a list of cases, at the minute, none of those are military.
"I've a full team working on the On The Runs review and that doesn't relate to the military at all.
"I do appreciate that in the public domain, the big profile cases that we've been working on have been in the area of military-related killings.
"We're carrying out our duties according to the law and according to what we've been asked to do and required to do."
The HET previously completed reviews of 1,625 cases, which related to 2,051 deaths.
The majority of the cases, 1,038, were attributed to republican paramilitaries, mostly the Provisional IRA.
Of the others, 536 cases were attributed to loyalists, 32 to the army, and it's not known who was responsible for the remaining 9.
There are no plans to re-investigate cases described as completed by the HET at this stage unless new evidence is uncovered.
Annan Athletic had to work hard for a gritty 1-0 win at East Stirlingshire with Josh Todd bagging the only goal.
[NEXT_CONCEPT]
Figures obtained by the BBC challenge claims that investigations into Troubles killings are unduly focused on those committed by the Army.