Her Christian Democrats (CDU) are on course to take 41%, comfortably seeing off a challenge by the Social Democrats (SPD), projected to secure 29.5%
Mrs Merkel is hoping for a fourth term as chancellor.
The centre-left SPD has seen a recent surge in popularity under new leader Martin Schulz.
Polls closed at 16:00 GMT in Saarland - a small south-western state with one million inhabitants.
The state is currently governed by a coalition of the CDU and SPD as junior partner, mirroring the national government.
A Deutschlandtrend poll for national TV on 24 March suggested the CDU and the SPD were on level pegging nationally, but that voters favoured Mr Schulz to lead the next government in Berlin.
The former president of the European Parliament took up the post as leader of the SPD in January. He is credited with a revival in popular support for his party.
In Saarland, a recent survey indicated a narrow lead for the CDU, but there had been predictions that a coalition between the SPD, the far-left Linke and the environmentalist Greens may emerge.
Exit polls showed Mrs Merkel's party's fetching 41% from 35.2 percent in the last election in 2012.
Meanwhile, the SPD's vote went down slightly from 30.6% and the Greens failed to reach the 5% threshold to enter the state assembly.
However, the populist right-wing Alternative for Germany (AfD), which has played on dissatisfaction with Mrs Merkel's policy on immigration, did succeed in winning seats in the Saarland legislature with 6% of the vote.
Ace shot-putter - the SPD's Anke Rehlinger
The state contest saw Saarland's prime minister, 54-year-old Annegret Kramp-Karrenbauer, go up against her deputy in the regional government, the SPD's Anke Rehlinger, 40.
Mrs Rehlinger, a trained lawyer, has governed alongside Mrs Kramp-Karrenbauer since 2014. She holds the state record in shotput, 16.03m, and was a youth champion in discus.
Mrs Kramp-Karrenbauer has been prime minister of Saarland since 2011.
Experienced hand - Saarland's PM Annegret Kramp-Karrenbauer
Saarland, a mainly Catholic state bordering Luxembourg and France, has sought to transform itself into a magnet for hi-tech industry after the decline of coal mining.
The CDU has governed there since 1998.
The national election takes place on 24 September but more state elections, in Schleswig-Holstein and North Rhine-Westphalia, will be held before then.