The Northern Ireland international emerged as the unlikely hero, beating Villa goalkeeper
Christian Benteke then missed a golden chance to snatch a point for Villa, who has not won on the road in 13 English Premier League matches.
Fulham deserved its win, although Jol was frustrated his side had not converted one of its myriad of earlier chances to take control of the match.
Baird eventually popped up to score the winner with only his sixth career goal in his 200th league appearance.
"Baird is very good at attacking the near post, he is always close but he hasn't scored for as long as I have known him," Jol said.
"It was most probably the worst corner kick ever. I don't think it was a good delivery but because he attacked the ball he could score.
"It is about players being at the end of the delivery and it was nice to see Chris there.
"We should have scored a goal earlier. I thought we played really well for the first 15 minutes.
"After that they had too much possession for my liking. It was a result ground out by us but I don't care. We need the points.
"We have to be strong at home. I am very pleased."
Jol was forced to reshuffle his front line after
Dimitar Berbatov returned from a hip injury and made an immediate impression - far more so than Villa's returning striker
The only down side of Berbatov's performance, in Jol's mind, was that he did not hit the target with an audacious volley.
"I am very pleased. The forward-line had never played together before so to get a result like this is special for us," Jol said.
"(Berbatov's performance) would have been better if he had scored - normally he scores from volleys!
"He wants to take responsibility, he feels good, he loves the atmosphere at the training ground and it's a new challenge for him."
For Lambert, it was another dose of the away-day blues but he attempted to put a positive spin on the defeat.
"I thought some of the football we played was great. I thought we gave as good as we got," Lambert said.
"We came here, where their form has been really good, and gave a good account of ourselves.
"I thought we played well at Newcastle and Tottenham. The only game I have been disappointed at was Everton.
"There are a lot of good things. We have to turn the good things into wins."
Bent returned to the side in place of Benteke, after being dropped for the last two matches, but was ineffectual up front for Villa.
"Chris had two hard games with the national team. Darren was fresh, I thought Darren and Gabby (Agbonlahor) did fine.
"I thought he (Bent) did really fine. I thought him and Gabby worked well and worked hard together."
Benteke should have earned Villa a point but he put Charles N'Zogbia's cross wide from close range.
"From where I was standing I don't know how far away it was and how close the shot was. I don't know if it was a chance," Lambert said.
"He will be a big player for this club. He is in one hell of a national side at the minute and performing really well. He will be fine.
"He is a handful. He changes the dynamics of a game at certain times. He will be a big player for us. He has got years to go in his career."
English Premier League