Hernandez, 30, celebrated a rare start by scoring in each half with trademark poacher's finishes and Pellegrini hopes the Mexican can build on his performance following a stop-start season because of illness.
Yet the arrival of those late-comers coincided with the hosts falling behind in sloppy fashion. The Spaniard remains popular on Merseyside after winning the Champions League and FA Cup during six years in charge, but is less well-regarded at Chelsea despite winning the Europa League in his only season at the club.
The Brazilian winger played a key role in Saturday's comprehensive 3-0 win at Newcastle and with Cardiff and Crystal Palace both due at the London Stadium in the next week, is hopeful of establishing a real momentum.
What does it mean? Over their last four games, West Ham have picked up five points.
Javier Hernandez showed the Newcastle strikers how to do it, clinically converting two of his chances to set West Ham on the way towards victory. The Austria global found space time and time again in the first half and was also at the heart of West Ham's best efforts on the counter-attack prior to his 70th-minute withdrawal.
And the Magpies were wasteful in front of goal. Since then he has been playing some minutes here and there, but now he is in good shape.
Newcastle were looking for a fourth straight Premier League win but produced a lacklustre display and failed to take the chances they did create.
West Ham's £36million recruit Felipe Anderson - who scored the visitors' third goal - was outstanding in the game.
- Javier Hernandez has scored 48 Premier League goals with all of those strikes coming from inside of the box - only Tim Cahill (56) has scored more goals in the competition with 100 per cent of them coming from inside of the box.