Substitute Lita's glancing header from Barry Robson's free-kick on Tuesday night kept Boro on the coat-tails of the teams in the play-off places and left the Rams precariously perched just above the relegation zone.
The Teessiders had been reduced to 10 men shortly before when Rhys Williams was shown a second yellow card for a late challenge on Dean Leacock.
Boro had earlier gone ahead through Robson's superb opening goal after 15 minutes but Derby turned it around thanks to goals from substitute Chris Porter and Michael Tonge before Lita ensured the points were shared.
Robson's deflected free-kick from the right side of the area after four minutes had David Martin scrambling across his goal but the ball went wide of the far post.
At the other end, Danny Coyne pushed a driven shot from Rob Hulse behind for a corner after Tonge had seized on some sloppy midfield play by Boro.
Boro took the lead when Andrew Taylor's cross was only headed to the edge of the area by Nicky Hunt and Robson's rocket of a volley flew past Martin.
It was the Teessiders' first away goal in 313 minutes of league football since David Wheater scored in a 1-1 draw at Ipswich at the start of last month.
There were more chances at the beginning of the second half than the entire first 45 minutes, and they were all created by Boro.
Williams was denied by a brave block by Hunt before Scott McDonald and Chris Killen both narrowly missed with efforts from the edge of the box.
McDonald then curled a shot just wide of the far post from the left side of the area after 65 minutes.
So it was against the run of play when Derby equalised through Porter.
The former Motherwell man had only been introduced as a replacement for Robbie Savage four minutes previously when he headed in at the far post after Coyne could only push Jay McEveley's cross into his path.
Derby went ahead when Boro failed to clear their lines and Tonge crashed in a 20-yard volley that was equally as good as Robson's earlier effort.
Luke O'Neil sent a volley just wide as Boro searched for the equaliser.
It looked unlikely to come after Williams saw red but Lita got a touch to Robson's inswinging cross to earn a vital point.