Scott started his first match in a major international tournament alongside skipper Steven Gerrard in central midfield.
It was a typical all-action display from Scott, who earned his 14th cap in the Donbass Arena. He was eventually substituted in the 78th minute.
Jermain came on a minute earlier for Alex Oxlade-Chamberlain and didn't have a chance, but was involved in the build-up to a late chance, where James Milner's dangerous cross was eventually cleared at the near post. That was JD's 48th cap.
Joleon Lescott headed home the opener for England in the 29th minute, levelled by Samir Nasri's 20-yarder 10 minutes later.
Host nation Ukraine top Group D after a 3-1 win against Sweden on Monday night.
England return to action on Friday against Sweden, while Ukraine take on France.
The tournament continues on Tuesday with co-hosts Poland facing Russia and Greece against the Czech Republic.
The next Spurs interest is on Wednesday and a real cracker as Rafa van der Vaart's Holland cross swords with old rivals Germany. The Dutch will need a positive result after a surprise loss to Denmark in their opener.