Stephen Quinn enjoyed a dream debut for Hull to crank up the pressure on Bolton manager Owen Coyle, who admitted his side's fans were right to be upset with the performance.
Quinn, who signed from Sheffield United on transfer deadline day, capped off a fine display with Hull's third goal four minutes after Abdoulaye Faye had edged the hosts in front just after the interval.
However, Bolton were abject after Hull forward Sone Aluko had cancelled out Chris Eagles' opener, and the visiting fans vented their frustrations for long spells, with some calling for Coyle's departure.
"The fans are quite right to be unhappy," Coyle said.
"We all recognised the importance of hitting the ground running this season. We're a better team than four points from four games.
"We can talk about individual mistakes, but I've never been evasive and ultimately I'm the man responsible. If you finish the season in the way we did, that can sometimes feed negativity at the start of the next season.
"But there's no point feeling sorry for yourself and you need to go out there and do something about it.
Hull manager Steve Bruce hailed the impact of Quinn, who provided forward momentum to a side that had scored only one goal in their first three games of the season.
"It was a late deal to sign him, but we did fantastically to get him," Bruce said.
"I've been after him for a couple of years, even when I was at Sunderland, as I've always thought he was a very good player. We need more goals in the team and we were conscious of that when we signed him. We've come up with a new system and it suits him.