We present the first measurement of the two-particle transverse momentum differential correlation function, P2≡ ΔpTΔpT/ pT2, in Pb-Pb collisions at sNN=2.76 TeV. Results for P2 are reported as a function of the relative pseudorapidity (Δη) and azimuthal angle (Δφ) between two particles for different collision centralities. The Δφ dependence is found to be largely independent of Δη for |Δη|≥0.9. In the 5% most central Pb-Pb collisions, the two-particle transverse momentum correlation function exhibits a clear double-hump structure around Δφ=π (i.e., on the away side), which is not observed in number correlations in the same centrality range, and thus provides an indication of the dominance of triangular flow in this collision centrality. Fourier decompositions of P2, studied as a function of the collision centrality, show that correlations at |Δη|≥0.9 can be well reproduced by a flow ansatz based on the notion that measured transverse momentum correlations are strictly determined by the collective motion of the system.