Only second-bottom Luton Town have a lower tally than the Tigers's 41 league goals this season, and that goal-shy form seemed certain to continue after Lewie Coyle showed a lack of conviction to rival Palmer's astonishing misses when the ball fell kindly for him eight yards out with 16 minutes remaining.
The home fans made their agitation clear to a side appearing bereft of ideas and outclassed, but 21-year-old Kamara's third goal in eight league matches boosted their survival hopes.
As well as the three-point gap to the relegation zone, the Tigers have a goal superiority of at least 12 over any of the teams in the bottom three.
Coventry host West Brom on Friday in what is now an even more crucial fixture for both sides' promotion hopes.
Hull travel to 12th-placed Swansea City on the same day and host Preston North End on Monday, when Coventry visit bottom side Plymouth.
Hull manager Ruben Selles told BBC Radio Humberside:
"Coventry have been particularly good since Frank took over and we knew it would be a difficult game. We managed to be competitive, stayed in the game and created situations like the one for Kasey [Palmer] - we need to start to put those in.
"The game management we showed for the goal we conceded is something we need to stop and eradicate from our game - hopefully forever - because it's costing us points.
"The team showed character in the second half. The subs made a big impact and we managed to get the point and show we can be as competitive as anybody. I know what I have in my dressing room - they are competitors and doing everything for the club."
Coventry manager Frank Lampard told BBC CWR:
"At this stage of the season you have to take a point and accept it, but we deserved more. Our play was really good with just the end bit missing, at times.
"Our defensive game in the first half was really good. They created one chance but it was a foul on Ben Sheaf - other than that, there was no danger and we created a number of chances, particularly at 1-0.
"I'm really happy with the players and disappointed for them that we didn't get three points. No disrespect to Hull, who are a good team, but we played like a team playing for the play-offs and I enjoyed our performance."