diff --git a/vector/atlas.go b/vector/atlas.go
index 233bab3fd..abb23dc25 100644
--- a/vector/atlas.go
+++ b/vector/atlas.go
@@ -90,8 +90,13 @@ func (a *atlas) setPaths(dstBounds image.Rectangle, paths []*Path, bounds []imag
 		a.pathIndexToAtlasRegionIndex[r.pathIndex] = i
 	}
 
+	w, h := dstBounds.Dx(), dstBounds.Dy()
+	// For antialiasing, doubled regions in the X direction are used.
+	if antialias {
+		w *= 2
+	}
 	// Use 2^n - 1, as a region in internal/atlas has 1px padding.
-	maxImageSize := max(4093, dstBounds.Dx(), dstBounds.Dy())
+	maxImageSize := max(4093, w, h)
 
 	// Pack the regions into an atlas with a very simple algorithm:
 	// Order the regions by height and then place them in a row.
diff --git a/vector/util_test.go b/vector/util_test.go
index 23a4ed7b5..dfb899884 100644
--- a/vector/util_test.go
+++ b/vector/util_test.go
@@ -126,3 +126,23 @@ func TestFillRects(t *testing.T) {
 		t.Errorf("got: %v, want: %v", got, want)
 	}
 }
+
+// Issue #3377
+func TestFillRectOnBigImage(t *testing.T) {
+	dst := ebiten.NewImage(3000, 3000)
+	defer dst.Deallocate()
+
+	vector.FillRect(dst, 0, 0, 3000, 3000, color.White, true)
+	if got, want := dst.At(0, 0), (color.RGBA{0xff, 0xff, 0xff, 0xff}); got != want {
+		t.Errorf("got: %v, want: %v", got, want)
+	}
+	if got, want := dst.At(2980, 0), (color.RGBA{0xff, 0xff, 0xff, 0xff}); got != want {
+		t.Errorf("got: %v, want: %v", got, want)
+	}
+	if got, want := dst.At(0, 2980), (color.RGBA{0xff, 0xff, 0xff, 0xff}); got != want {
+		t.Errorf("got: %v, want: %v", got, want)
+	}
+	if got, want := dst.At(2980, 2980), (color.RGBA{0xff, 0xff, 0xff, 0xff}); got != want {
+		t.Errorf("got: %v, want: %v", got, want)
+	}
+}