Marc Bridge-Wilkinson made two changes at the break, with Alvin Ayman and Scofield Lonmeni emerging from the bench to great effect.
The hosts were now the dominant side, left-back Cam Williams making his mark with some excellent early crosses into the box.
Sonni-Lambie teed up Onanuga with a clever pass on 53 minutes and his powerful drive was saved by Alastair Graham in the Forest goal.
But the Reds midfielder was not to be denied two minutes later, collecting a superb pass over the top from Moran to beat Graham and start a stirring comeback.
Ayman next found fellow substitute Lonmeni via a clever pass and his shot was tipped over the bar by Graham as the home side built up the pressure.
It paid off on 69 minutes as a lovely team goal brought them back on terms. Sonni-Lambie played in Tyler Martin near the byline on the right and his perfect cross was tapped home by a grateful Bradshaw for goal No.14 of a breakthrough season.
There only looked to be one winner but all the good work was almost undone by a sloppy defensive pass and a Forest third looked inevitable until a superb block by Moran denied them at the last.
The centre-back was in action again just after, making another vital interception in front of his own goal, with the ball ricocheting away off the post.
Liverpool had claims for a late penalty for handball turned away by the referee and despite several opportunities, they had to settle for a point.
**Team**
Misciur, Airoboma, Williams, Moran, Owen, Upton (Ayman, 46), Bradshaw, O'Connor (Lonmeni, 46), Sonni-Lambie, Onanuga (Ahmed, 85), Martin.
Unused subs: Enahoro-Marcus, Bernard.
Goals: Onanuga (55), Bradshaw (70).
**Next up**
The Reds are in U18 Premier League North action again next Saturday (March 15). They travel to face Wolverhampton Wanderers in a 12pm GMT kick-off at the Sir Jack Hayward Training Ground.