diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md
index 139e123ec..ab63d5faa 100644
--- a/docs/CHANGELOG.md
+++ b/docs/CHANGELOG.md
@@ -21,6 +21,7 @@ The following tip changes can be tested by building VictoriaMetrics components f
 * FEATURE: [vmalert](https://docs.victoriametrics.com/vmalert.html): allow configuring the default number of stored rule's update states in memory via global `-rule.updateEntriesLimit` command-line flag or per-rule via rule's `update_entries_limit` configuration param. 
 
 * BUGFIX: [vmui](https://docs.victoriametrics.com/#vmui): properly update the `step` value in url after the `step` input field has been manually changed. This allows preserving the proper `step` when copy-n-pasting the url to another instance of web browser. See [this issue](https://github.com/VictoriaMetrics/VictoriaMetrics/issues/3513).
+* BUGFIX: properly parse floating-point numbers without integer or fractional parts such as `.123` and `20.` during [data import](https://docs.victoriametrics.com/#how-to-import-time-series-data). See [this issue](https://github.com/VictoriaMetrics/VictoriaMetrics/issues/3544).
 
 
 ## [v1.85.3](https://github.com/VictoriaMetrics/VictoriaMetrics/releases/tag/v1.85.3)
diff --git a/go.mod b/go.mod
index 0bfa4d145..c9f3de7ae 100644
--- a/go.mod
+++ b/go.mod
@@ -26,7 +26,7 @@ require (
 	github.com/klauspost/compress v1.15.13
 	github.com/prometheus/prometheus v0.41.0
 	github.com/urfave/cli/v2 v2.23.7
-	github.com/valyala/fastjson v1.6.3
+	github.com/valyala/fastjson v1.6.4
 	github.com/valyala/fastrand v1.1.0
 	github.com/valyala/fasttemplate v1.2.2
 	github.com/valyala/gozstd v1.17.0
diff --git a/go.sum b/go.sum
index de9090ece..bb1c3b761 100644
--- a/go.sum
+++ b/go.sum
@@ -425,8 +425,8 @@ github.com/urfave/cli/v2 v2.23.7/go.mod h1:GHupkWPMM0M/sj1a2b4wUrWBPzazNrIjouW6f
 github.com/valyala/bytebufferpool v1.0.0 h1:GqA5TC/0021Y/b9FG4Oi9Mr3q7XYx6KllzawFIhcdPw=
 github.com/valyala/bytebufferpool v1.0.0/go.mod h1:6bBcMArwyJ5K/AmCkWv1jt77kVWyCJ6HpOuEn7z0Csc=
 github.com/valyala/fasthttp v1.30.0/go.mod h1:2rsYD01CKFrjjsvFxx75KlEUNpWNBY9JWD3K/7o2Cus=
-github.com/valyala/fastjson v1.6.3 h1:tAKFnnwmeMGPbwJ7IwxcTPCNr3uIzoIj3/Fh90ra4xc=
-github.com/valyala/fastjson v1.6.3/go.mod h1:CLCAqky6SMuOcxStkYQvblddUtoRxhYMGLrsQns1aXY=
+github.com/valyala/fastjson v1.6.4 h1:uAUNq9Z6ymTgGhcm0UynUAB6tlbakBrz6CQFax3BXVQ=
+github.com/valyala/fastjson v1.6.4/go.mod h1:CLCAqky6SMuOcxStkYQvblddUtoRxhYMGLrsQns1aXY=
 github.com/valyala/fastrand v1.1.0 h1:f+5HkLW4rsgzdNoleUOB69hyT9IlD2ZQh9GyDMfb5G8=
 github.com/valyala/fastrand v1.1.0/go.mod h1:HWqCzkrkg6QXT8V2EXWvXCoow7vLwOFN002oeRzjapQ=
 github.com/valyala/fasttemplate v1.2.2 h1:lxLXG0uE3Qnshl9QyaK6XJxMXlQZELvChBOCmQD0Loo=
diff --git a/vendor/github.com/valyala/fastjson/fastfloat/parse.go b/vendor/github.com/valyala/fastjson/fastfloat/parse.go
index 5d4a7c7a7..b37838da6 100644
--- a/vendor/github.com/valyala/fastjson/fastfloat/parse.go
+++ b/vendor/github.com/valyala/fastjson/fastfloat/parse.go
@@ -213,6 +213,12 @@ func ParseBestEffort(s string) float64 {
 		}
 	}
 
+	// the integer part might be elided to remain compliant
+	// with https://go.dev/ref/spec#Floating-point_literals
+	if s[i] == '.' && (i+1 >= uint(len(s)) || s[i+1] < '0' || s[i+1] > '9') {
+		return 0
+	}
+
 	d := uint64(0)
 	j := i
 	for i < uint(len(s)) {
@@ -232,7 +238,7 @@ func ParseBestEffort(s string) float64 {
 		}
 		break
 	}
-	if i <= j {
+	if i <= j && s[i] != '.' {
 		s = s[i:]
 		if strings.HasPrefix(s, "+") {
 			s = s[1:]
@@ -263,7 +269,9 @@ func ParseBestEffort(s string) float64 {
 		// Parse fractional part.
 		i++
 		if i >= uint(len(s)) {
-			return 0
+			// the fractional part may be elided to remain compliant
+			// with https://go.dev/ref/spec#Floating-point_literals
+			return f
 		}
 		k := i
 		for i < uint(len(s)) {
@@ -363,6 +371,12 @@ func Parse(s string) (float64, error) {
 		}
 	}
 
+	// the integer part might be elided to remain compliant
+	// with https://go.dev/ref/spec#Floating-point_literals
+	if s[i] == '.' && (i+1 >= uint(len(s)) || s[i+1] < '0' || s[i+1] > '9') {
+		return 0, fmt.Errorf("missing integer and fractional part in %q", s)
+	}
+
 	d := uint64(0)
 	j := i
 	for i < uint(len(s)) {
@@ -382,7 +396,7 @@ func Parse(s string) (float64, error) {
 		}
 		break
 	}
-	if i <= j {
+	if i <= j && s[i] != '.' {
 		ss := s[i:]
 		if strings.HasPrefix(ss, "+") {
 			ss = ss[1:]
@@ -413,7 +427,9 @@ func Parse(s string) (float64, error) {
 		// Parse fractional part.
 		i++
 		if i >= uint(len(s)) {
-			return 0, fmt.Errorf("cannot parse fractional part in %q", s)
+			// the fractional part might be elided to remain compliant
+			// with https://go.dev/ref/spec#Floating-point_literals
+			return f, nil
 		}
 		k := i
 		for i < uint(len(s)) {
diff --git a/vendor/modules.txt b/vendor/modules.txt
index 2b5468a98..ffc54c938 100644
--- a/vendor/modules.txt
+++ b/vendor/modules.txt
@@ -447,7 +447,7 @@ github.com/urfave/cli/v2
 # github.com/valyala/bytebufferpool v1.0.0
 ## explicit
 github.com/valyala/bytebufferpool
-# github.com/valyala/fastjson v1.6.3
+# github.com/valyala/fastjson v1.6.4
 ## explicit; go 1.12
 github.com/valyala/fastjson
 github.com/valyala/fastjson/fastfloat