You're supposed to drain the wort from the mash, then add sparge water.
I use my boil kettle to heat sparge water too. For now what I do is pour the sparge water into a 5gal cooler, place the mash tun on top of the 5gal cooler (for height), drain the wort from the mash into the kettle, place the mash tun on the floor, pour the appropriate amount of sparge water from the 5gal cooler into the mash tun, let sit for 10 min, drain into kettle.
I'm looking forward to having another kettle with a ball valve for the HLT, it'll save me so much hassle and pouring of hot liquids.