Center And Zoom function using ArcGIS API for JavaScript?

I just finished doing something very similar so perhaps this will help you. I'm not using map.setExtent though (except as a fallback). Instead I'm using map.centerAndZoom. Right after I add the graphic, I have this bit of code. I'm thinking this may point you in the right direction (instead of maxZoom, you may be able to plug that zoom level 6 in?). One other difference is that I'm using a graphics layer ("esri/layers/GraphicsLayer") and adding the graphic to that instead of directly to map.graphics. Try adding this (after my comment line) after you add the graphic to the map.

EDIT: I do also have this line further up in the script.

var mp = webMercatorUtils.webMercatorToGeographic(evt.mapPoint);

graphicsLayer = new GraphicsLayer();  
graphicsLayer.add(graphic);  

map.addLayer(graphicsLayer);
// Add this bit of code after adding your graphic, 
if (graphic.geometry.type === 'point') {  
    maxZoom = map.getMaxZoom();  
    map.centerAndZoom(graphic.geometry, maxZoom - 1);  
} else {  
    map.setExtent(graphicsUtils.graphicsExtent([graphic]));        
} // end if

EDIT: I took out the second else per your commment. I was doing this nested inside a second if block that tests for the presence of a comma in a string entered by a user (lat, long) and the first if is testing for the index of the ",". I don't know what else you would need to do because this is working for me.