The triumph nudged Aitor Karanka’s men ahead of Derby in the promotion chase, but condemned Ian Holloway’s third-bottom side to their fourth defeat in five.
Patrick Bamford opened the scoring with his 11th goal of the season after 26 minutes and Kike made it two just four minutes later, with Belgian striker Jelle Vossen completing a routine win for the Teessiders 12 minutes from time.
Millwall had looked the brighter of the two sides early on, but it was Boro who were more dangerous on the break.
Kike fluffed a great chance in the 15th minute when Adam Clayton curled a ball into the box only for the striker to head straight at David Forde.
The Lions almost grabbed the opener just seconds later after Boro’s defence fell asleep. Lee Gregory latched onto a ball over the top but Dimi Konstantopoulos denied the striker with his legs.
Boro had three bites at the cherry after 20 minutes, but still failed to open the scoring. Kike and Albert Adomah both had shots blocked before Tomlin’s goal-bound effort was brilliantly cleared off the line by Alan Dunne.
The game really opened up as the visitors continued to press and, when Boro failed to clear a corner, Joss Hooiveld had time to turn and shoot but it was easy enough for Konstantopoulos to gather.
The hosts got their opener in the 26th minute, though, with a neat build-up and well-taken finish. Tomlin played in Adomah, who pulled it back for Kike and he let the ball roll to Bamford, who coolly hammered it into Forde’s top-right corner.
Karanka’s men doubled their lead on the half-hour mark when Clayton’s long ball found Bamford in the box and he did well to lay off for Kike, who tried his best to miss but the ball bounced over Forde’s head and in.
They went close to a third shortly after half-time when Adomah raced down the left wing before over-hitting his cross for Grant Leadbitter and the Boro skipper headed over.
Tomlin was left fuming with Kike on the hour when the Spaniard opted to shoot instead of passing – his effort was deflected wide for a corner.
Adomah went close to getting the third when Leadbitter picked him out with a perfect set-piece into the box but Forde did well to hold the winger’s strong shot.
Boro again went close in the 73rd minute when George Friend did well down the left before cutting inside and crossing across the face of goal, but it was just too strong for Kike.
The third goal finally arrived five minutes later after Friend’s shot was deflected into Vossen’s path and he drilled past Forde.