The visitors missed a host of chances before Beram Kayal poked home his first goal for the club in first-half stoppage time to leave second-placed Rangers needing to beat Aberdeen on Wednesday to keep on their bitter rivals shoulders.
St Johnstone improved after the break but their players, who haven't scored in the league for 70 days, were always going to find it hard to get back on level terms when they had to play the final minutes with ten men after Chris Millar hobbled off injured after Saints had used all three substitutes.
The game ended in farcical scenes when referee Iain Brines ignored Celtic's penalty claims after substitute Michael Duberry handled the ball in the box but it mattered not a jot as Celtic held on for the three points.
"It was a game I was pretty concerned about but I felt we went about our business very well," said Lennon, who returned to his place in the dugout following his four match ban after the disgraceful scenes at the end of Celtic's Cup win over Rangers last month.
"I was delighted with the three points and delighted with the performance and really, with better finishing, it could have been more comfortable."
His St Johnstone counterpart Derek McInnes said it had been a committed performance.
"We didn't carry as much threat as we wanted but I felt we dealt with them for the majority of the game and restricted them to few opportunities.
"In the main we were always in the game but we're just disappointed to lose a goal just before half-time."
Lennon restored captain Scott Brown to his starting line-up along with Mark Wilson, Joe Ledley, Kris Commons, Georgios Samaras and Daryl Murphy.
With one eye on their Scottish Cup semi-final clash with Motherwell on Saturday McInnes made seven changes for the match.
It was Murphy, in his first start since December, who set up Samaras for the game's first chance but the Greek blasted his shot well over.
Smith subsequently superbly blocked Samaras' low shot with his legs before the keeper finally conceded in first-half stoppage time.
Brown's pass was knocked into the path of Kayal by St Johnstone's Steve May and despite being off balance the Israeli international poked the ball past Smith with the outside of his right foot.
St Johnstone started the second-half the brighter of the two teams but it took until the hour mark for them to test Fraser Forster when the keeper had to be alert to turn Liam Craig's fierce left foot shot round the post.
Celtic appealed for a penalty in the 86th minute when Duberry appeared to handle the ball in the box after the Englishman thought referee Iain Brines had awarded him a free-kick following a barge from Samaras but the referee bizarrely waved away Celtic's claims.
Brown then cracked a shot off the underside of the crossbar and Smith saved Maloney's headed rebound on the line as Celtic finished strongly.
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