Mr Hogg had unveiled his proposals last week saying that accepting the Government's tax freeze deal would damage frontline policing.
His budget plan, which will maintain police officer numbers at more than 3,000 while also retaining 380 community support officers and recruiting an extra 50 "specials" a year, was though subject to the approval of the Devon and Cornwall Police and Crime Panel.
It met in Plymouth yesterday, and after a two-and-a-half hour debate, which included discussion of Mr Hogg's strategic crime plan, passed the tax increase by 15 votes to one.
"We believed that not raising the police part of the council tax during the next financial year would have a major impact on policing in Devon, Cornwall and the Isles of Scilly," Mr Hogg said after the decision.
"It would have meant that officer numbers may have fallen to well below 3,000.
"We are working hard to maintain officer numbers at their current levels and there was a real need for the force to increase funds to be able do this."
The decision means that the police share of council tax bills for Band D properties will rise by £3.19 to £162.92 next year – the second lowest rate in the South West and slightly below the national average.
With £4.3 million being taken from reserves, the total budget for 2013-14 will be £288.6 million.
Mr Hogg added: "The budget is there to make sure the police force in Devon and Cornwall is fit for the future and the many challenges they face.
"An essential element of today is our effort to halt or arrest the decline in police officer numbers for as long as we can.
"There were Government options in terms of funding which we declined to take this time because it is really important that we build the foundations of the funding base for policing going forward.
"It enables us to arrest the decline in police officer numbers and therefore have higher visibility because these are the things that the public really want.
"It also enables us to invest in policing, in technology and training, and in the public service we offer. So, in the round, to me it is an excellent decision.
"It is now up to us to deliver a high standard of policing."
In the last two years Devon and Cornwall Police has shrunk from 3,500 to 3,100 officers, with more than 500 civilian staff also being cut as the force saved £32 million to meet Government targets.
The plan, with a further £7.5 million savings to be found in 2013-14, had been to keep reducing officer strength, eventually falling to 2,800 – a level last seen in the 1980s.
While the 2% hike was approved against Government pressure to keep bills down, Mr Hogg's budget report had painted a grim picture of taking the Government's offer of freezing council tax in exchange for a 1% increase in grant.
It would have left the force with just 125 officers on neighbourhood policing to cover communities spread over 4,000 square miles.
Mr Hogg also predicted a "critical reduction in pro-active crime reduction" and in police visibility.
The commissioner's police and crime plan, in which Mr Hogg has pledged to put victims at the heart of, was also discussed at length by the panel.
It shone a light on another reorganisation of the force, to a "geographical" model which it tore up in May 2010 to move to the "functional" model which promised to deliver the necessary savings.
What went with it was the traffic department, with busy response officers expected to patrol the network when they were not dealing with 999 calls.
The changes have coincided with a worrying increase in fatal accidents although senior officers have always denied that the two are linked.
Mr Hogg, however, yesterday alluded to a possible U-turn by the constabulary with 120 officers "being biased towards roads policing but without creating a traffic department" but did not elaborate further.
