diff --git a/python/core/auto_generated/geometry/qgsrectangle.sip.in b/python/core/auto_generated/geometry/qgsrectangle.sip.in
index 1dae45d63e5..a7ab241c917 100644
--- a/python/core/auto_generated/geometry/qgsrectangle.sip.in
+++ b/python/core/auto_generated/geometry/qgsrectangle.sip.in
@@ -183,6 +183,13 @@ Scale the rectangle around its center point.
     void scale( double scaleFactor, double centerX, double centerY );
 %Docstring
 Scale the rectangle around its center point.
+%End
+
+    QgsRectangle scaled( double scaleFactor, const QgsPointXY *center = 0 ) const;
+%Docstring
+Scale the rectangle around its ``center`` point.
+
+.. versionadded:: 3.4
 %End
 
     void grow( double delta );
diff --git a/src/core/geometry/qgsrectangle.cpp b/src/core/geometry/qgsrectangle.cpp
index a5c7884b1e7..cd54b82def1 100644
--- a/src/core/geometry/qgsrectangle.cpp
+++ b/src/core/geometry/qgsrectangle.cpp
@@ -58,6 +58,13 @@ QgsRectangle QgsRectangle::fromCenterAndSize( QgsPointXY center, double width, d
   return QgsRectangle( xMin, yMin, xMax, yMax );
 }
 
+QgsRectangle QgsRectangle::scaled( double scaleFactor, const QgsPointXY *center ) const
+{
+  QgsRectangle scaledRect = QgsRectangle( *this );
+  scaledRect.scale( scaleFactor, center );
+  return scaledRect;
+}
+
 QgsRectangle QgsRectangle::operator-( const QgsVector v ) const
 {
   double xmin = mXmin - v.x();
diff --git a/src/core/geometry/qgsrectangle.h b/src/core/geometry/qgsrectangle.h
index 81202f6c4dd..61db526e12e 100644
--- a/src/core/geometry/qgsrectangle.h
+++ b/src/core/geometry/qgsrectangle.h
@@ -261,6 +261,12 @@ class CORE_EXPORT QgsRectangle
       mYmax = centerY + newHeight / 2.0;
     }
 
+    /**
+     * Scale the rectangle around its \a center point.
+     * \since QGIS 3.4
+     */
+    QgsRectangle scaled( double scaleFactor, const QgsPointXY *center = nullptr ) const;
+
     /**
      * Grows the rectangle in place by the specified amount.
      * \see buffered()
diff --git a/src/gui/qgsmapcanvas.cpp b/src/gui/qgsmapcanvas.cpp
index 0210e04a895..caf69850656 100644
--- a/src/gui/qgsmapcanvas.cpp
+++ b/src/gui/qgsmapcanvas.cpp
@@ -996,8 +996,40 @@ void QgsMapCanvas::zoomToSelected( QgsVectorLayer *layer )
   }
 
   rect = mapSettings().layerExtentToOutputExtent( layer, rect );
+
+  // zoom in if point cannot be distinguished from others
+  // also check that rect is empty, as it might not in case of multi points
+  if ( layer->geometryType() == QgsWkbTypes::PointGeometry && rect.isEmpty() )
+  {
+    int scaleFactor = 5;
+    QgsPointXY center = mSettings.mapToLayerCoordinates( layer, rect.center() );
+    QgsRectangle extentRect = mSettings.mapToLayerCoordinates( layer, extent() ).scaled( 1.0 / scaleFactor, &center );
+    QgsFeatureRequest req = QgsFeatureRequest().setFilterRect( extentRect ).setLimit( 1000 ).setNoAttributes();
+    QgsFeatureIterator fit = layer->getFeatures( req );
+    QgsFeature f;
+    QgsPointXY closestPoint;
+    double closestSquaredDistance = extentRect.width() + extentRect.height();
+    bool pointFound = false;
+    while ( fit.nextFeature( f ) )
+    {
+      QgsPointXY point = f.geometry().asPoint();
+      double sqrDist = point.sqrDist( center );
+      if ( sqrDist > closestSquaredDistance || sqrDist < 4 * std::numeric_limits<double>::epsilon() )
+        continue;
+      pointFound = true;
+      closestPoint = point;
+      closestSquaredDistance = sqrDist;
+    }
+    if ( pointFound )
+    {
+      // combine selected point with closest point and scale this rect
+      rect.combineExtentWith( mSettings.layerToMapCoordinates( layer, closestPoint ) );
+      rect.scale( scaleFactor, &center );
+    }
+  }
+
   zoomToFeatureExtent( rect );
-} // zoomToSelected
+}
 
 void QgsMapCanvas::zoomToFeatureExtent( QgsRectangle &rect )
 {
diff --git a/tests/src/core/testqgsrectangle.cpp b/tests/src/core/testqgsrectangle.cpp
index 4ace39739cb..3d43aba2422 100644
--- a/tests/src/core/testqgsrectangle.cpp
+++ b/tests/src/core/testqgsrectangle.cpp
@@ -40,6 +40,7 @@ class TestQgsRectangle: public QObject
     void isFinite();
     void combine();
     void dataStream();
+    void scale();
 };
 
 void TestQgsRectangle::isEmpty()
@@ -348,5 +349,22 @@ void TestQgsRectangle::dataStream()
   QCOMPARE( result, original );
 }
 
+void TestQgsRectangle::scale()
+{
+  QgsRectangle rect( 10, 20, 30, 60 );
+  rect.scale( 2 );
+  QCOMPARE( rect, QgsRectangle( 0, 0, 40, 80 ) );
+  rect.scale( .5 );
+  QCOMPARE( rect, QgsRectangle( 10, 20, 30, 60 ) );
+  QgsPointXY center( 10, 20 );
+
+  // with center
+  rect.scale( 2, &center );
+  QCOMPARE( rect, QgsRectangle( -10, -20, 30, 60 ) );
+
+  // scaled
+  QCOMPARE( rect, QgsRectangle( 10, 20, 30, 60 ).scaled( 2, &center ) );
+}
+
 QGSTEST_MAIN( TestQgsRectangle )
 #include "testqgsrectangle.moc"