Pablo Hernandez and Gianni Alioski struck goals in either half to put Leeds 2-0 up before Britt Assombalonga ensured a nervous finale by converting a controversial 76th-minute penalty.
When asked if victory had seen Leeds turn a corner, Christiansen said: "Yes of course. The team is alive. They have been the whole time, believing in taking the three points always."
Leeds had slipped from top of the table to 11th after losing six of their previous seven league games, but are back up to seventh, level on points with Middlesbrough.
"When you fail you have to work harder and during these two weeks we have analysed a lot, worked a lot and there has been a good atmosphere in the team," Christiansen said.
The Leeds boss said he had no sympathy for Boro counterpart Garry Monk, who endured a miserable first return to Elland Road.
Monk quit at the end of May and was given a hostile reception by a large section of Leeds fans in a crowd of 33,771.
"No. Garry or me, we are not playing," Christiansen said. "It's the players who have to respond on the pitch.
"The attitude of the players, their willingness to go for the win from the first whistle - that was the difference in this game."
Christiansen refused to dwell on referee Keith Stroud's decision to award Boro a 76th-minute penalty, which ensured a frantic finale.
Luke Ayling and Daniel Ayala had grappled in the area before a corner and after consulting with one of his assistants, Stroud pointed to the spot.
"It was a foul for us," Christiansen added. "The good thing in this sense was the reaction the players had, this responsibility that they took on the pitch. That proved we are working well."
Monk, who quit Leeds two days after owner Andrea Radrizzani completed his takeover, played down the Leeds fans' abuse.
"That wasn't even my focus," he said. "It wasn't about me. It's about my team and the players on the pitch and we're disappointed with the result and should have got more.
"It's not about me. What's happened has happened. I've said my side, the club has said their side and that's done and dusted.
"I've great memories of this club and enjoyed my season here, but now I'm at Middlesbrough and my only focus is on them."
Monk, whose side came in to the game on the back of three successive league wins, felt they did not deserve to lose.
"There weren't many clear-cut chances for either team," he added. "But I think we definitely did enough to at least take a point away from this game."