The pressure had been building on West Brom after four games without a win either side of the three-month hiatus, with the Baggies failing to score in any of those matches.
Wednesday's 3-0 victory over Sheffield Wednesday lifted a lot of weight off Bilic's shoulders, then, as Albion maintained a five-point advantage on the chasing pack.
West Brom now stand six games away from a Premier League return, with half of those games against teams battling relegation.
That is the case for Hull, who are two points above the relegation zone thanks to a massive win of their own last time out.
The Tigers recovered from a goal down to beat fellow strugglers Middlesbrough 2-1 at the KCOM Stadium on Thursday, Mallik Wilks snatching the points in the 93rd minute.
The late goal from Wilks brought an end to City's 15 match winless run in all competitions, 13 of those coming in the league in a run stretching back to New Year's Day.
From being a couple of points outside the playoff zone to relegation favourites, it has been quite the slump in form for Grant McCann's men.
They now have a platform to build on, though, and will be looking to gain some momentum ahead of games with Wigan Athletic and Luton Town in the next few weeks.
However, Hull have lost four and won none of their last six away games in the Championship since a 1-0 victory at Sheffield Wednesday in early January.
Interestingly, three of City's last five league goals on the road have come via a header - only one of their previous 20 away goals this season had been scored that way.
West Brom have hardly been in the best of form at The Hawthorns, though, having won just two of their last nine home league fixtures, failing to score in the last two of those.
West Brom's Championship form: WLDDLW
West Brom's form (all competitions): LLDDLW
Hull City's Championship form: LLLLDW
Versatile full-back Nathan Ferguson has not started since the Championship resumed last month and he has been ruled out of this game.
That is Albion's only confirmed absentee following the return to fitness of Grady Diangana, who played nearly an hour against Wednesday but may drop out here.
Hull are likely to be without Herbie Kane for this match as the Liverpool loanee limped off shortly after scoring against Middlesbrough.
Wilks, Hull's other goalscorer against Boro, should retain his place out on the right after signing a permanent contract with the Tigers this week.
West Brom possible starting lineup:
Johnstone; O'Shea, Hegazi, Ajayi, Gibbs; Livermore, Sawyers; Grosicki, Pereira, Robinson; Austin
Hull City possible starting lineup:
Long; Pennington, Wijs, Burke, Fleming; Wilks, Batty, Stewart, Scott; Lopes; Magennis
We say: West Brom 2-0 Hull City
Both teams will be looking to build on big midweek victories. Hull have lost their last three away matches against promotion-chasing West Brom and we are expecting that run to continue this weekend.