Indian national Bijukumar Remadevi Nair Gopinathan was sentenced for killing a Filipino prostitute in a Singapore hotel in 2010.
As per the previous provisions, the law stipulated mandatory death sentence for all categories of murder, The Straits Times said.
Similarly, Malaysian Jabing Kho was sentenced to death for the murder of a Chinese national in 2008.
The two are first from the death row to have their cases heard by the High Court under the revised law.
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As of October last year, 34 prisoners were given a lifeline under the revised law, the daily said.
Amid no objection from the prosecution, lawyers for these two convicts applied separately to the Court of Appeal yesterday for their cases to be sent back for re-sentencing.
The High Court will hear their arguments on whether they should be handed the death sentenced penalty at a later date, and the decision is open for appeal.
Death penalty under the revised law is only mandatory for Section 300 (a) under the revised law, compared to being mandatory for any categories of murder previously.
However in September last year, his conviction under Section 300 (a) was quashed by the Court of Appeal.
Kho, 26, had killed 40-year old Chinese national Cao Ruyin while robbing him in 2008. He was convicted in 2010 and his appeal was dismissed in 2011.