The Dutch midfielder exchanged passes with Andy Hunt before firing a low shot past Ian Bennett from the edge of the box with eight minutes left.
Birmingham dominated the game, only to be left cursing a host of missed chances. They were denied time and again by Albion's goalkeeper, Alan Miller. "I've been saying for a while how well the team are playing and the level of performance again today was very, very good and spirited,'' Francis said.
"We've passed the ball, we created opportunities and I think only three members of our team have not had an opportunity to score. I think the first 45 minutes was as one-sided as I've seen since I came to the club and when you are playing that well you expect to go in two or three nil up. As individuals I think every one of my team can look at their performance and say they played well."
Birmingham's Paul Furlong was lucky to stay on after he was booked for not retreating 10 yards at a free-kick and then appeared to catch Paul Mardon with an elbow as the pair jumped for a high ball inside the first two minutes. But after that early scare the visitors took control.
Steve Bruce - back in the City side after he was dropped for the last three away games - saw his header from a Chris Marsden corner saved by Miller before Furlong's follow-up shot was also blocked.
Michael Johnson shot well wide when unmarked inside the Albion box and Steve Robinson fired wide of an empty net.
Marsden then wasted a great chance in the 27th minute when he shot tamely at Miller and the Albion goalkeeper then pulled off a stunning one-handed stop to deny Jon McCarthy.
Albion's first chance came after 38 minutes when Kevin Kilbane squared the ball but no-one was on hand to follow up. Then, on the stroke of half- time, Robinson again went close to giving Blues the lead but his 20-yard shot flashed just wide.
Birmingham started the second half on top and Miller again had to be alert to save from McCarthy after the winger had skipped past several defenders.
Mardon produced a superb goal-line clearance in the 63rd minute after Furlong had chipped the ball over the stranded Miller - and 60 seconds later the Baggies' keeper had to tip Martin Grainger's free-kick over the bar. He made another superb save after 78 minutes when he tipped Robinson's 20-yard drive wide before Sneekes struck.
Birmingham hit back immediately and Grainger flashed one shot wide and had another well saved by Miller before Furlong headed inches off target from eight yards out. But West Bromwich hung and their manager, Ray Harford, said: "I have got to feel sorry for Trevor. Birmingham played very well. It was Miller who won us the game. I've definitely got to accept that Birmingham deserved to win."
Goal: Sneekes 83 (1-0).
West Bromwich Albion: Miller, Holmes, Smith, Sneekes, Burgess, Mardon, Flynn (Hughes, 52), Hamilton, Butler, Hunt, Kilbane. Substitutes not used: Coldicott, Dobson.
Birmingham City: Bennett, Bass, Grainger, Bruce, Ablett, Marsden, McCarthy, Robinson, Furlong, Cottee (Ndlovu, 80), Johnson (Devlin, 88). Substitutes not used: Hughes.
Referee: S Bennett (Redhill).
Booked: West Bromwich: Holmes, Hughes. Birmingham: Marsden, Furlong.
Man of the match: Miller.
Attendance: 18,444.Reuse content