Converted first-half scores from captain Paul O'Connell and scrum-half Mike Phillips, and three Owen Farrell penalties put them 23-3 up at half-time.
Phillips' second try took the Lions 30-3 clear before Kahn Fotuali'i replied for the Baa-Baas.
Further scores from Jonathan Davies, Alex Cuthbert (two), Dan Lydiate and Alun Wyn Jones took the Lions way ahead of their flagging components.
Farrell kicked his opening penalty after two minutes, but not before he was charged down by his Barbarian Nick Evans.
A controversial moment when hooker Schalk brits launched at Farrells face. englishman Farrell responded but fortunately didn't connect.
The Lions then won a penalty at a scrum 10 metres from the Baas line, but Farrell pulled it wide.
Wasps centre Elliot Daly landed a superb 45-metre penalty to bring the Baa-Baas level.
The staccato nature of the contest continued with every scrum in the first half resulting in a free-kick or penalty for the Lions, Farrell kicking the Lions 6-3 ahead from one.
After the impressive Richie Gray's pass just eluded Stuart Hogg metres from the line, and O'Connell cut inside rather than releasing Maitland in space outside him, the Lions got their opening try in the 28th minute.
After a series of pick-and-drives, Phillips poweried through a gap and holding off Bayonne team-mate Joe Rokocoko's tackle to score.
Farrell converted both tries, and a sweetly-struck long-range penalty with the last kick of the half gave the Lions a 23-3 interval lead.
Richard Hibbard found Lydiate at the tail with a perfect throw on the resumption, and the flanker's tap down saw Phillips dummy and sprint through for his second try.
Justin Tipuric was denied a try by Rokocoko's superb tackle, and the Lions might have scored one of the great tries in their history after a length-of-the-field counter attack, only for Farrell's try-scoring pass to Maitland to be intercepted.
Instead, after a poor pass from Farrell to Davies gave the Baa-Baas a first sniff, Rokocoko stretched his legs, stood up Toby Faletau and released replacement Fotuali'i for a try.
But it was a brief riposte, Davies pouncing for a poacher's try immediately, before Faletau and Jamie Roberts sent Cuthbert racing in for the fifth.
The giant Wales wing celebrated his first outing since 16 March with a second score after a smart break from Irish replacement scrum-half Conor Murray.
Amid a flurry of changes on both sides, James Hook came on for the Barbarians to become only the second player - after Riki Flutey - to play for and against the Lions.
All in all a fantastic victory for the Lions and an exciting start to their tour down under.