After a disastrous first half where Marcos Alonso and Thiago Silva mistakes gifted goals for Callum Robinson and Kyle Bartley, Lampard threw on Azpilicueta and Hudson-Odoi for Alonso and midfielder Mateo Kovacic.
Both had hands in goals as Chelsea staged a fightback.
Azpilicueta laid the ball off to Mason Mount who scored from distance, before Hudson-Odoi neatly worked his way through the West Brom defence in order to claw a second back.
In the third minute of added time, Tammy Abraham levelled things up to earn the Blues a point when they were staring down the barrel of defeat.
While Lampard was hugely frustrated by the individual mistakes, he singled out both Azpilicueta and Hudson-Odoi for special praise, hailing the character of the Spaniard and the technical quality of the young England international.
‘Azpi brings personality straight into the team even at left-back and Calum brought one v one something different,’ Lampard told Sky Sports after the match.
‘[He] got at people, things that Callum needs to do and can do because of his talent so he made a big difference.’
Hudson-Odoi told the BBC: ‘At 3-0 we wanted to try to get the points and had the feeling that we would get the goals.
‘It was good, we worked hard, got the ball wide early, kept playing and got the goals.
‘The new boys have gelled really well. All worked hard. They’ve improved us and have shown they are quality players with the right mentality to win games.’