With Tambling watching from the stands, Lampard hit his 201st goal for the Blues shortly after setting up Oscar for the strike that put Rafael Benitez's side ahead in the 44th minute at Stamford Bridge.
The win strengthened Chelsea's grip on a top four place, moving them three points clear of Tottenham who lie fifth with just four games remaining.
The match also marked referee Mark Clattenburg's first appearance at the Bridge since he was cleared of racially abusing John Obi Mikel during Chelsea's defeat to Manchester United last October.
Clattenburg's return passed off with little controversy, although Benitez and his players were convinced Swansea captain Ashley Williams should have received a second yellow card midway through the second half.
The referee's decision not to punish Williams for pulling back Demba Ba made little difference to the outcome however, with Chelsea easing their way to victory against a Swansea team with little to play for.
Benitez's side came into the game on the back of Thursday's impressive victory in Basle in the first leg of their Europa League semi-final.
That result moved the Blues closer to a second successive European final following last year's Champions League triumph, but Benitez has always maintained a place in the top four is the club's main priority.
And Chelsea's hopes of securing a place in next season's Champions League were lifted ahead of this clash by Tottenham's failure to beat Wigan 24 hours earlier.
But there were few signs the prospect of putting clear water between themselves and the White Hart Lane club had provided any extra motivation during a tepid opening.
A long-range drive from Ba brought a smart save from Swansea keeper Michel Vorm while at the other end Ashley Cole's acrobatic block prevented Michu's header from testing Petr Cech, but otherwise there were few early opportunities.
Lampard's introduction in place of the injured Ramires in the 28th minute injected more urgency into Chelsea's play and the midfielder declared his intentions with a powerful run from halfway and shot that again brought Vorm into action.
And from the resulting corner, Gary Cahill, back in the starting line-up after undergoing minor knee surgery, headed just over.
Cahill was partnered in central defence by John Terry, who retained his starting place as Benitez broke with his policy of rotating the club captain.
And Terry, who revealed last week his intention to reverse his decision to retire from international football, contributed to Oscar's opening goal that came in the 43rd minute.
The centre back collected the ball after a poor Swansea clearance, finding Lampard who released Oscar on the right hand side of the Swansea area and the Brazil international finished with a clinical right foot shot across Vorm and inside the far post.
With half time fast approaching, Lampard killed off Swansea's resistance from the penalty spot after Juan Mata had been tripped by Leon Britton.
Chelsea had come to life at exactly the right time and there was little chance of Swansea repeating their success in the League Cup semi-final over the Blues.
Benitez's men remained in control, content to see out the game, although they should have added to their tally from one of a number of openings.
Ba again made Vorm work with another long-range shot but the best chance of the second period fell to Mata, who collected Eden Hazard's low cross and sent an angled shot inches wide of the right hand post.
The miss was never likely to matter and Chelsea were able to run down the clock before switching their attention to Thursday's visit from Basle in the Europa League.