Goel was challaned near Raisina Road, on his way to Parliament.
Central government ministers will remain exempt from odd-even scheme while CM Arvind Kejriwal and his cabinet colleagues will come under the ambit of the second phase.
More people are expected to hit the roads after celebrating the New Year and an extended weekend.
Besides pressing into service 3,000 additional buses, the government has issued two helplines -- 011-42400400 and 011-41400400 -- for people to register their complaints and suggestion in connection with the scheme.
Around 125 teams of the Transport and Revenue departments will be deployed during the 15-day plan so that the scheme could be effectively implemented.
After driving autorickshaws and BMWs, Telangana native Vankadarath Saritha has become the first woman to hit the Delhi roads as a DTC driver.
CNG cars have been kept out of the ambit of the odd-even scheme while a decision on whether women drivers will continue to be exempted will be taken soon.
Terming as "unconstitutional and illegal" Aam Aadmi Party's national council meeting where they were ousted from a key panel, dissidents Yogendra Yadav and Prashant Bhushan on Saturday did not rule out taking legal recourse against their removal.
Gearing up to roll out the ambitious odd-even scheme, Delhi government on Thursday said an additional fleet of 6,000 buses will be deployed to enhance public transport.
Under interim measures, there will be no renewal of registration of diesel vehicles which are more than 10 years old.
The pattern came up a few times during Kejriwal's 40-minute-long speech, where he highlighted his government's "achievements", punctuated with loud cheers from the students.
Only four-five lawmakers availed of the facility of DTC's "MP Special" to reach Parliament on the first day of the launch of the service.
Delhi Police Commissioner B S Bassi appreciated the initiative of the Aam Aadmi Party government, saying any step which helps the environment cannot be a bad thing and asserted he will ensure full implementation.
Aam Aadmi Party founder members Yogendra Yadav and Prashant Bhushan, who had challenged Arvind Kejriwal's leadership, were removed from the party's powerful national executive by an overwhelming majority at the national council meet on Saturday
Congress leader Anand Sharma said the scheme was coming in the way of MPs discharging their duties and not being able to attend the meetings of Parliamentary Committees due to it.
Similar traffic restrictions in other cities did not see a significant improvement in air quality only because car owners begin making more trips during their unrestricted periods. The other apprehension, as seen in other cities, is that residents have bought secondhand cars, using the other number plate so that they can continue to drive to their work place, thereby defeating the very purpose of this scheme.