Taylor's second-half goal secured back-to-back wins for Bolton
Matthew Taylor struck the only goal as Bolton picked up their second win in six days but condemned Hull to their third straight Premier League defeat.
Taylor scored with a left-foot strike from the edge of the area that went through a crowd of players.
Marlon King hit the woodwork for Hull while Bolton keeper Jussi Jaaskelainen made a great double save from Geovanni.
The keeper parried from King late on and brilliantly recovered to punch the ball clear with Geovanni again lurking.
Bolton were cheered to their victory by a sizeable away contingent, fully justifying the club's decision to lay on free coach travel to their fans.
Before their victory over Manchester City last Sunday, Gary Megson's team had won only once since the opening day of the season.
Megson praises 'top-class goalkeeping'
But their first back-to-back victories since April sees them move clear of the relegation zone and into mid-table.
Hull boss Phil Brown spent 15 years on the coaching staff at Bolton but it was not a happy reunion for the Tigers manager as he saw his team lose a game in which they had more than enough chances to earn at least a point.
However, Hull could find no way past a goalkeeper in sensational form, with Jaaskelainen pulling off a series of brilliant saves on his 400th start for the club.
His late effort to thwart King after the striker's shot had taken a deflection before scrambling off the turf to once again deny Geovanni typified his performance.
However, the match itself was far from a classic and the first half in particular was a largely forgettable affair, only sporadically enlivened by the occasional outbreak of brilliance or excitement.
It took almost 15 minutes for the first half-decent effort at goal, Geovanni forcing Jaaskelainen into action with a decent strike from 20 yards.
Hull were inches away from breaking the deadlock when King audaciously flicked a cross from the left towards goal with the back of his heel. The ball looped over the stranded Jaaskelainen but rebounded off the woodwork.
For large parts of the half it was Bolton who looked more comfortable in possession and they worked the ball well through midfield without creating any clear-cut openings.
Brown finds positives in defeat
The closest they came followed hesitation in the Hull defence, with Ricardo Gardner nipping in between keeper and defender before crossing the ball into the six-yard box. However, there were no Bolton players on hand to knock it into an empty net and the Tigers cleared the danger.
Early in the second half, though, Bolton did score when Taylor hit the ball past the unsighted Boaz Myhill after the home team had failed to clear a corner.
An attritional phase of play followed, with both teams desperate to score the crucial next goal.
Jaaskelainen saved free-kicks from Andy Dawson and Geovanni - but it was his amazing double save from Geovanni that really caught the eye.
The Brazilian seemed certain to head home a free-kick but Jaaskelainen somehow kept the ball out - and when it came back into the danger zone Geovanni, on the floor, hooked it towards goal from two yards but the Finnish keeper again denied him.
Jaaskelainen then made his double save from King and Geovanni as the visiting team, who had been without suspended skipper Kevin Nolan, held on for a valuable away win.
Hull manager Phil Brown on Jussi Jaaskelainen's impressive performance:
"He's had a blinder. He pulled off a couple of great saves, with the one from the Geovanni header the turning point.
"But he had one of those days, although he is a world-class 'keeper anyway, and I've nothing but admiration for him.
"He is certainly one of the best in the Premier League, and that's the standard we have to attain."
Bolton boss Gary Megson on Jaaskelainen:
"He will get the headlines, and rightly so because his performance was unbelievable, as good as you are ever going to see.
"Some of his saves, like the one from the free kick - which was bad defending from ourselves - at point-blank range was good enough. But to then spring onto his feet and palm it away from the other forward coming in was top-class goalkeeping.
"There are some good goalkeepers throughout the world, and we certainly wouldn't swap him for anybody.
"He is not just a terrific goalkeeper, but a good lad, a good pro, and everything that comes his way he deserves because he works his socks off in training."
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