Rewards of gift vouchers, extra holidays and cash bonuses are being given to Home Office staff who help prevent failed asylum seekers from staying in the country.
Immigration officers have a target of winning 70% of tribunal cases in which asylum seekers are appealing against government decisions that they should leave the UK, and are offered the incentives as part of Home Office reward schemes, the Guardian said.
The Home Office said the voucher scheme applied to all staff at the department, not just those working on asylum cases.
Rewards of high street shopping vouchers for £25 or £50 were given to presenting officers and case owners working in the areas of asylum and immigration, the newspaper said, which the Home Office said were to "recognise positive performance over a short period of time", such as when officers exceed monthly casework targets.
The revelations came following requests made under Freedom of Information laws.
A parliamentary answer in November revealed 11 vouchers for £25 have been given out since July 2012 to presenting officers in asylum cases as a "one-off recognition of individual performance at court".
Mark Harper, a Home Office minister, said vouchers were not awarded for solely winning a case, but for factors such as quality of preparation and advocacy.
He said: "Presenting officers' performance is managed in accordance with the same performance management policy that applies to all Home Office staff.
"Where an officer's overall performance is judged to be unsatisfactory, the Home Office's poor performance procedure may be instigated."
Sarah Teather, a Liberal Democrat MP and former minister, told the newspaper the scheme completely undermined any sense that asylum seekers would receive a fair hearing.
She said: "If the Home Officer are really giving out shopping vouchers for officers who help ensure asylum seekers lose their appeals that is a new low."
Duncan Lewis, a firm of immigration solicitors, believes some cases with strong grounds for appeal are withdrawn by the Home Office on the day of the tribunal because officials fear they will lose and miss their targets.
The firm told the Guardian it was considering a legal challenge the voucher scheme suggested a "clear incentive to bad practice".
A Home Office spokesman said: "It is not true that individual officers prioritise cases that are most likely to succeed and any decision to withdraw a case has to be approved at a more senior level.
"The success of our officers in upholding asylum decisions is only one of a range of criteria we use to monitor staff performance. All our staff are expected to meet appropriate professional standards."
Shadow immigration minister David Hanson said: "It's unacceptable that the Government is using gimmicks and playing with people's lives to mask the incompetence of the Home Office.
"Theresa May needs to get a grip on her department, clear the backlogs and ensure the right decisions are made first time.
"Evidence of the impact of immigration on the UK needs to be published and asylum claims should be dealt with on merit and quickly, but under Theresa May the length of time it takes to complete reviews has increased and the backlog is getting longer, costing the taxpayer money and keeping families in limbo.
"Rather than deal in gimmicks such as ineffective rewards which could foster unfairness in life-changing decisions, the Government needs to immediately take steps to ensure a speedy and fair resolution of asylum claims."