In a startling display, Townsend scored the opener and then set-up Brazil's Paulinho to open his Spurs account before laying a third on a plate for Roberto Soldado.
Soldado bagged another while young left-back Danny Rose scored his first for Spurs since netting on his debut against Arsenal in April 2010.
The result in this play-off first leg tie has all but rendered next week's second leg at White Hart Lane meaningless and should see the English Premier League side safely into the Europa League group stages.
Townsend started off the rout when latching onto a ball cleared Spurs' box following a Dinamo corner.
Kyle Naughton played the ball to Townsend, who raced 50 yards before firing low past goalkeeper George Loria from 25 yards in the 11th minute.
Iceland midfielder Gylfi Sigurdsson almost doubled the advantage when curling a free-kick from outside the area into the side-netting but the second goal did come two minutes before the break.
Naughton, again, released the lively Townsend down the right with a delicately chipped past and the winger turned inside his marker before picking out Paulinho's late run into the box with a perfect dinked cross, allowing the Brazilian to head simply home from six yards.
Townsend was at it again when he scampered down the right in the 57th minute, using his pace to reach the byline before picking out Soldado for a simple tap-in at the near post.
And it could have been more as Paulinho lost his bearings with an overhead bicycle kick after Townsend's delightful chip picked him out.
The respite for Dinamo was brief as Rose curled the pick of the bunch into the top corner from 20 yards on 65 minutes while three minutes later Soldado had another tap-in from six yards after substitute Nacer Chadli's fizzing cross from the left.
Spurs could have made it six after Harry Kane's header from another inviting Chadli cross came back off the post seven minutes from time.
Swans trounce Petrolul Ploiesti
It was a great night for the English Premier League as Swansea City trounced Romanians Petrolul Ploiesti 5-1 in Wales.
Wayne Routledge started the ball rolling, scoring a pair of first half goals either side of Spaniard Michu's close range toe poke.
And Ploiesti's Brazilian goalkeeper Picanha scored an unfortunate own goal to compound matters in the second half, elbowing the ball over the line after he had initially saved Wilfried Bony's near post flick.
Alejandro Pozuelo rounded off matters 20 minutes from time with a clever dink over the grounded Picanha after Michu's through ball.
But the goal of the night came from Ploiesti's Gheorge Grozav three minutes from time with a stunning overhead bicycle kick from the edge of the area that earned him a standing ovation from the Swansea crowd.
Ukraine giants Dynamo Kiev won 3-2 at Kazakhs Aktobe Lento while Russians Rubin Kazan won 2-0 at Ole Gunnar Solskjaer's Molde.
Betis triumph in Jablonec, Dynamo Kyiv win in Aktobe
In other early games, Jorge Molina and Cedric scored as Real Betis triumphed 2-1 at Czech outfit Jablonec, for whom Jan Kopic hit the net.
And Ukraine giants Dynamo Kyiv won 3-2 at Kazakhs Aktobe Lento while Russian Rubin Kazan won 2-0 at Ole Gunnar Solksjaer's Molde.
Former European Cup winners Feyenoord lost 1-0 at Russians Kuban Krasnodar while France's Saint-Etienne, finalists in 1976, were beaten 4-3 at Danes Esbjerg.