They were both on target on Sunday as Chelsea outclassed Southampton 2-0 to move into fourth spot with 22 points -- just one behind Manchester City, Arsenal and Liverpool.
The poor form and questionable appetite of both Costa and Hazard was blamed partly for Chelsea's dire start to last season that ultimately cost manager Jose Mourinho his job.
However, the duo who helped fire Chelsea to the 2014-15 title are thriving once again in Antonio Conte's 3-4-3 system.
Hazard's opener after six minutes meant he has scored in three consecutive Premier League games and has five for the season. This time last year he had failed to register and did not score his first league goal until April.
Likewise, Costa, looking again like the marauding bruiser who ran defences ragged when he first arrived at Stamford Bridge rather than the disinterested figure he cut early last season, already has eight league goals to his credit.
It took him until January to reach that total last season and he had managed just two in the league when Mourinho was sacked.
His second-half effort, a curling shot from 25 metres, was sublime but it was his work rate across the pitch that rubbed off on the Spain international's team mates.
"When you see Eden and Diego, and Pedro, working very hard during the game, you are happy," Conte said of his front three.
"They are strikers and usually it's a bit difficult for the strikers to work for the team, but their commitment and work-rate is fantastic."
Chelsea's defending too has been unrecognisable this season. They have conceded nine goals compared to the 19 they had already leaked after 10 games under Mourinho a year ago.
Even with skipper John Terry fit to return on Sunday, Brazilian David Luiz was again preferred alongside Gary Cahill and Cesar Azpilicueta and did not put a foot out of place.
"I'm very happy after this performance. I saw great commitment, work rate -- with the ball and without it. For the fourth game we keep a clean sheet, it's fantastic," Conte said.
"It's early for us to speak about title contenders. We have to work very hard to continue. We can improve a lot. We must improve."
(Reporting by Martyn Herman; Editing by Ian Chadband)
