Baroda ended the day at 376/4 as they lost only three wickets in the entire day. Swapnil Singh (63 not out) and Abhijit Karambelkar (8 not out) were at the crease when stumps were drawn.
But it was Waghmode, who hogged the limelight as he hit 13 fours and a six in his knock which came off 309 deliveries.
The visitors took control of the game, Mumbai's 500th Ranji clash, after bundling out the hosts for a partly 171 in their first innings.
Waghmode built partnerships with Solanki and Hooda as Baroda went on piling the runs with the Mumbai attack looking lacklustre.
It was Shreyas Iyer who accounted for Waghmode, who was caught by Ajinkya Rahane with the score board reading 355-4.
But till then the left-handed opener had helped Baroda pass the 350-run-mark and take a healthy lead.
For Mumbai, Shardul Thakur, Royston Dias, Iyer and Vijay Gohil took a wicket each.
Brief scores: Mumbai first innings- 171 all out, Baroda - first innings 376/4: Aditya Waghmode - 138, Deepak Hooda (75); Royston Dias (1-16), Shreyas Iyer (1-22).
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)