More than half of adults in Scotland who are certain to vote on May 7 (52%) said they would vote SNP, against 24% backing Labour, the TNS poll of 978 adults in Scotland found.
The 28-point lead is nearly double last month's figure, when the parties scored 46% and 30% respectively.
The Conservatives scored 13% (down one percentage point), the Liberal Democrats 6% (up three points) and the Greens 3% (down one point).
Support for Ukip in Scotland is "almost negligible", TNS said. The survey covered the period of the UK-wide TV debates, although it closed before the impact of the Scottish leaders' TV debates could be taken into account.
Tom Costley, head of TNS Scotland, said: "The official election campaign has got off to a great start for the SNP, undoubtedly helped by Nicola Sturgeon's strong performance in the UK-wide TV debate. Not only has Labour's hopes of a recovery in support been dashed but, even worse, it appears to have gone backwards.
"The SNP seems to be building on the momentum which they carried forward from the independence referendum, while Jim Murphy is still struggling to win back Labour's lost supporters. Indeed, the latest poll shows some evidence that the growth in SNP support is mainly coming from disaffected Labour supporters.
"But it's important to remember that the campaign is really only beginning and 29% of those who say they are certain to vote have not made up their minds who to vote for. It will be interesting to see what difference the campaigns of the various parties make to people's intentions by polling day."
Support for the SNP continues to be very strong among younger voters who are certain to vote and express a preference - 71% of 18 to 34-year-olds, against 57% for 35 to 54-year-olds and 40% for those aged 55 and over. Among the oldest age group, Labour scores 32% and the Conservatives 20%.
However, fewer of the younger voters say they are certain to vote - 52% of 18 to 34-year-olds against 67% overall.
In the event of a hung parliament, 44% of Scottish voters would prefer a Labour-led government compared with 15% who back a Tory-led administration.
The most popular single option is a Labour-SNP coalition, with 25% support.
Both parties have ruled this out, but the response suggests that some form of SNP-Labour co-operation has significant backing, TNS said.
The next most popular option is 9% for the continuation of a Conservative-Liberal Democrat coalition.
Nearly a third (31%) of Labour voters would prefer the option of co-operating with the SNP, while 28% opted for a Labour minority government.
If the SNP holds a majority of Scotland's 59 seats in a hung parliament, voters are evenly divided between those who want the SNP to work with Labour (34%) and those who want the SNP to remain a separate bloc in the Westminster Parliament (32%).
SNP voters are also evenly divided - 42% want to work with Labour and 45% would want the party to remain separate.
TNS surveyed 978 adults aged over 18 across Scotland between March 18 and April 8.