The Argentine, making his first start of the season after suffering knee and thigh problems, blasted home a 64th minute penalty just as the Rams appeared to be heading for another defeat.
And then with minutes to go and the Kent club threatening once again to breach the home defence, Zavagno saved a certain goal in tackling Marlon King three yards from goal as the striker had looked set for a simple finish.
On balance, a point was a fair result as the cultured prompting and probing from Derby's Georgi Kinkladze was cancelled out by the Gills' more direct and muscular style of play.
The first half took some time to get going but it was Kinkladze who came closest to scoring when his exquisite left-foot curler struck the post and rebounded to safety.
If that was unfortunate then Derby keeper Lee Grant enjoyed a rather better slice of luck when he ran 40 yards from goal to tackle King as the striker raced clean through.
Two debatable penalty decisions went against the home side as twice Malcolm Christie - possibly playing his last game for the club in the face of interest from Middlesbrough - was felled by challenges from Barry Ashby.
Ipoua ignored the cries for offside to steer a fierce shot across Grant into the bottom corner.
Seconds later, and with Riggott and Christie now withdrawn through injury, the visitors had a glorious chance to seal the game but from a similar position King could not beat Grant.
Derby hauled themselves back when Morris was scythed down by Ashby and Nicky Southall and Zavagno scored his first goal for the club.
A frantic finale saw Morris, Kinkladze and Adam Bolder all fail to hit the target while Grant pulled off a miracle stop from King as both sides looked for the win.