After scoring four tries for a second successive game, Tigers retained top spot in the Guinness Premiership, but only after some last-ditch defence with just 12 men following yellow cards for Henry and Alesana Tuilagi, and injury to Scott Bemand when all of the replacements had been used.
The final whistle blew after referee Wayne Barnes ruled that Bath's Eliota Fuimaono-Sapulo had been held up over the Tigers try-line deep in injury time.
Head coach Pat Howard said: "The last tackle was Johne Murphy, and Paul Burke got underneath him, but there were some fantastic efforts across the board in terms of defence.
"After we conceded a soft try before half-time, they got momentum, they got some penalties and Olly Barkley was kicking well. But the guys did very well and I am proud of them.
"In the last two games we have scored eight tries and conceded three, although they have still been pretty tight efforts. You have to be happy with scoring that many tries. The penalties are the only down side, I have got to sit down with referees and have a look at that."
Forwards coach Richard Cockerill was also proud of the efforts from the team, especially against such a strong a Bath pack.
"The forward battle was key, we knew that before the game that they were going to take us on with the pack they picked," Cockerill said. "They have a lot of strength throughout the forwards - Gareth Delve and Andy Beattie on the bench are both good players, they have Test locks, a Test prop and were only missing Lee Mears.
"To take them on shows the character of the players. Some of the guys might not be first choice when we are at full strength, but they pushed their claims and showed there is plenty of spirit to battle.
"Along with Graham Rowntree, I work a lot with the front-row guys and moments like that late scrum when we were missing players are what I call your money shots. You see what the players have inside them and today they proved they have got plenty.
"Tom Croft, for instance, is not the biggest second row and has not played there a lot this year, but he turned in a fantastic performance against two Test locks and that shows the potential of the player."
