Hiddink is yet to suffer defeat, but Chelsea have hardly been the dominant force of last season since Mourinho's December departure.
They have won only two and drawn three of their five Premier League games under Hiddink, including a 2-2 draw against the Baggies last night.
Failure to win means that no side has lost more points from leading positions this season than Chelsea (12 - level with Bournemouth and Newcastle). They only dropped 15 throughout 2014-15.
The Blues would have overtaken West Brom had they won, but a draw means that the champions are 14th in the table, six above the drop zone and double that to the top four.
Of Chelsea's 21 league matches, 12 have seen the Blues concede at least two goals and in total they have let in 31 - more than ever before at this stage of a Premier League season.
Recent Premier League form: LWDDWD
Recent form (all competitions): WDDWWD
This will be Everton's seventh match in three weeks since Christmas and they will continue to come thick and fast in the rest of the month, with the Capital One Cup semi-final second leg against Man City and an FA Cup fourth-round tie away at either Carlisle United or Yeovil Town to come.
After beating City 2-1 in the first leg of the aforementioned semi earlier in January, the Toffees again faced Manuel Pellegrini's side last night, holding them to a somewhat fortunate goalless draw.
Leon Osman was centimetres from scoring an outstanding first-half volley, but Everton can count themselves a little lucky to have not given away a late penalty when John Stones slid in on Raheem Sterling.
In goal, Tim Howard was under plenty of pressure after some iffy performances of late, but he turned in arguably his best display of the season to prevent City scoring in a league game at home for the first time in almost a year.
Last night's draw means that Roberto Martinez's men have lost just one of their 10 Premier League away games this season (at leaders Arsenal), although six of those games have been draws, including in four of the last five trips.
However, the big Belgian still needs just two goals to match his best Premier League goal tally for a season (17 in 2012-13 while on loan at West Brom).
Recent Premier League form: DLWLDD
Recent form (all competitions): WLDWWD
Eden Hazard missed the visit of West Brom and he is likely to sit out again on Saturday with a groin strain.
Pedro should continue in the Belgian's place, although Brazilian youngster Kenedy might get a look-in after he replaced Pedro at half time last night and played a part in the Blues' second goal.
As for the visitors, Martinez has no new injury concerns but might be able to welcome back Tom Cleverley from injury.
Other changes are unlikely as the Toffees have an eight-day gap before their next match and Stones should again play at right-back with Seamus Coleman still out.
Chelsea possible starting lineup:
Courtois; Ivanovic, Zouma, Terry, Azpilicueta; Mikel, Fabregas; Willian, Oscar, Pedro; Costa
Everton possible starting lineup:
Howard; Stones, Funes Mori, Jagielka Baines; Besic, Barry, Osman; Barkley, Deulofeu; Lukaku
Head To Head
However, Everton have not won in their last 20 Premier League matches at Stamford Bridge, losing 11 and drawing nine.
In fact, Chelsea have won their last two home games 1-0 against Everton with goals scored in the 89th and 90th minute and Roberto Martinez has lost on all six Premier League trips to Stamford Bridge as an opposition coach.
We say: Chelsea 2-2 Everton
It's tough to pick a winner here with neither team in particularly good form. Barring Everton's stalemate at the Etihad, both teams have been among the goals of late and an entertaining draw could be on the cards.