Hazard made it 2-0 with a penalty at the start of the second half after the in- form midfielder had been tripped and a deflected Pedro shot in stoppage time completed a great day for the Londoners.
Chelsea's 12th victory took the winning run past the 11 they managed in 2009 and left them within two of the top-flight record set by Arsenal in 2002.
The current Arsenal side unsurprisingly made all the running at home against West Brom but lacked spark for long spells.
Alexis Sanchez hit the post and West Brom's defenders made a series of desperate interventions until their resistance was broken by Giroud's header four minutes from time.
Manchester United were in command all day against Sunderland as former boss David Moyes returned to Old Trafford but the game remained tense until the latter stages as the hosts missed a series of chances.
Zlatan Ibrahimovic set up Daley Blind to fire in the opener in the 39th minute but inspired goalkeeping by Jordan Pickford prevented further damage until Ibrahimovic slotted the second in the last 10 minutes after a neat pass from the impressive Paul Pogba.
Henrikh Mkhitaryan completed a fifth straight win for United when he cleverly flicked in the third before Fabio Borini grabbed a last-minute consolation for Sunderland.
Champions Leicester City continued to struggle as they were beaten 2-0 at home by Everton and it was another uncomfortable day for Bob Bradley as his Swansea side were crushed 4-1 at home by West Ham United.
Burnley edged further away from the danger zone with a 1-0 win over fellow- strugglers Middlesbrough and Sam Allardyce's first match as Crystal Palace manager ended in a 1-1 draw at Watford.
- AAP
